Answer Show
Hint:- In 8 years money from Interest will be come equal to the principal Let the initial amount of money invested will be Rs. x. So, now we will use a simple interest formula. So, putting the values in the above formula. We will get, Hence, the rate of interest to double a money in 8 years will be 12.5% per annum. Note:- Whenever we came up with this type of problem where we are asked
to Important Points :OR Interest = Amount – Principal => S. I. = A – P Rules:RULE 1: Simple Interest (S.I.)= \( \frac{Principal * Rate * Time}{100} \) RULE 2: If there are distinct rates of interest for
distincttime periods i.e. RULE 3: If a certain sum becomes ‘n’ times of itself in T years on Simple Interest, then the rate per cent per annum is, RULE 4: If a certain sum becomes n1
times of itself at R1% rate and n2 times of itself at R2% rate, then, RULE 5: If Simple Interest (S.I.) becomes ‘n’ times of principal i.e. RULE 6: If an Amount (A) becomes ‘n’ times of certain sum (P) i.e. RULE 7: If the
difference between two simple interests is ‘x’ calculated at different annual rates and times, then principal (P) is RULE 8: If a sum amounts to x1 in t years and then this sum amounts to x2 in t yrs. Then the sum is given by RULE 9: If
a sum with simple interest rate, amounts to ‘A’ in t1 years and ‘B’ in same t2 years, then, RULE 10: If a sum is to be deposited in equal instalments, then, RULE 11: To find the rate of interest under current deposit plan, RULE 12: If certain sum P amounts to Rs. A1 in t1 years at rate of R% and the same sum amounts to Rs. A2 in t2 years at same rate of interest R%. Then, RULE 13: The difference between the S.I. for a certain sum P1 deposited for time T1 at R1 rate of interest and another sum P2
deposited for time T2 at R2 rate of interest is TYPE-IQ.1 What sum of money must be given as simple interest for six months at 4% per annum in order to earn ₹150 interest? ₹5000 ₹7500 ₹10000 ₹15000 Ans . 2
Q.2 A sum of ₹1600 gives a simple interest of ₹252 in 2 years and 3 months. The rate of interest per annum is: 5\( \frac{1}{2}\) 8% 7% 6% Ans . 2
Q.3 A sum of money lent at simple interest amounts to ₹880 in 2 years and to ₹920 in 3 years. The sum of money (in rupees) is 700 760 784 800 Ans . 4
Q.4 At some rate of simple interest, A lent ₹6,000 to B for 2 years and ₹1,500 to C for 4 years and received ₹9,00 as interest from both of them together. The rate of interest per annum was 5% 6% 8% 10% Ans . 1
Q.5 A lent ₹5000 to B for 2 years and ₹3000 to C for 4 years on simple interest at the same rate of interest and received ₹2200 in all from both as interest. The rate of interest per annum is 7% 5% 7\( \frac{1}{8}% \) 10% Ans . 4
Q.6 What sum of money will amount to ₹520 in 5 years and to ₹568 in 7 years at simple interest ? ₹410 ₹120 ₹510 ₹220 Ans . 1
Q.7 ₹500 was invested at 12% per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the sum of the interest on both the sum after 4 years is ₹480, the latter sum of money is : ₹450 ₹750 ₹600 ₹550 Ans . 3
Q.8 A money lender finds that due to fall in the annual rate of interest 8% to 7\( \frac{3}{4} \)%, his yearly income diminishes by ₹61.50. His capital is ₹22400 ₹23800 ₹24600 ₹26000 Ans . 3
Q.9 A lends ₹2500 to B and a certain sum to C at the same time at 7% annual simple interest. If after 4 years, A altogether receives ₹1120 as interest from B and C, the sumlent to C is ₹700 ₹6500 ₹4000 ₹1500 Ans . 4
Q.10 A certain sum of money amounts to ₹756 in 2 years and to ₹873 in 3\( \frac{1}{2} \) years at a certain rate of simple interest. The rate of interest per annum is 10% 11% 12% 13% Ans . 4
Q.11 What sum will amount to ₹7000 in 5 years at 3\(\frac{1}{3}\)% simple interest ? ₹6300 ₹6500 ₹6000 ₹5000 Ans . 3
Q.12 A man took a loan from a bank at the rate of 12% per annum at simple interest. After 3 years he had to pay ₹5,400 as interest only for the period. The principal amount borrowed by him was : ₹2000 ₹10000 ₹20000 ₹15000 Ans . 4
Q.13 A sum of money at simple interest amounts to ₹1,012 in 2\( \frac{1}{2} \)years and to ₹1,067.20 in 4 years. The rate of interest per annum is : 2.5% 3% 4% 5% Ans . 3
Q.14 A sum of money lent out at simple interest amounts to ₹720 after 2 years and to ₹1020 after a further period of 5 years. The sum is : ₹500 ₹600 ₹700 ₹710 Ans . 2
Q.15 The sum of money, that will give ₹1 as interest per day at the rate of 5% per annum simple interest is ₹3650 ₹36500 ₹730 ₹7300 Ans . 4
Q.16 If the simple interest on a certain sum of money for 15 months at 7\(\frac{1}{2}\)% per annum exceeds the simple interest on the same sum for 8 months at 12\(\frac{1}{2}\)% per annum by ₹32.50, then the sum of money (in ₹) is : 312 312.50 3120 3120.50 Ans . 3
Q.17 What annual instalment will discharge a debt of ₹6450 due in 4 years at 5% simple interest ? ₹1500 ₹1835 ₹1935 ₹1950 Ans . 1
Q.18 In what time will ₹72 become 81 at 6\(\frac{1}{4}\)% per annum simple interest ? 2 years 3 years 2 years 6 months None of these Ans . 1
Q.19 The simple interest on ₹7,300 from 11 May, 1987 to 10 September, 1987 (both days included) at 5% per annum is ₹123 ₹103 ₹200 ₹223 Ans . 1
Q.20 A person borrows ₹5,000 for 2 years at 4% per annum simple interest. He immediately lends it to another person at 6\(\frac{1}{4}\)% per annum simple interest for 2 years. His gain in the transaction is ₹112.50 ₹450 ₹225 ₹150 Ans . 3
Q.21 A man had ₹16,000, part of which he lent at 4% and the rest at 5% per annum simple interest. If the total interest received was ₹700 in one year, the money lent at 4% per annum was ₹12000 ₹8000 ₹10000 ₹6000 Ans . 3
Q.22 ₹1,000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become ₹2,000 after 15 years 18 years 20 years 16\(\frac{2}{3}\) years Ans . 4
Q.23 A sum of money amounts to ₹5,200 in 5 years and to ₹5,680 in 7 years at simple interest. The rate of interest per annum is 3% 4% 5% 6% Ans . 4
Q.24 ₹800 becomes ₹956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will ₹800 become in 3 years ? ₹1020.80 ₹1025 ₹1052 ₹1050 Ans . 3
Q.25 A person deposited ₹400 for 2 years, ₹550 for 4 years and ₹1,200 for 6 years. He received the total simple interest of ₹1,020. The rate of interest per annum is 10% 5% 15% 20% Ans . 1
Q.26 Manoj deposited ₹29400 for 6 years at a simple interest. He got ₹4200 as interest after 6 years. The annual rate of interest was 2\(\frac{8}{21}\)% 2\(\frac{7}{20}\)% 3\(\frac{8}{21}\)% 4\(\frac{8}{21}\)% Ans . 1
Q.27 A man lent ₹60,000, partly at 5% and the rest at 4% simple interest. If the total annual interest is ₹2560, the money lent at 4% was ₹40000 ₹44000 ₹30000 ₹45000 Ans . 2
Q.28 A sum of money at some rate of simple interest amounts to ₹2,900 in 8 years and to ₹3,000 in 10 years. The rate of interest per annum is 4% 2\(\frac{1}{2}\)% 3% 2% Ans . 4
Q.29 herIn how many years will a sum of ₹3,000 yield a simple interest of ₹1,080 at 12% per annum ?e 3 years 2\(\frac{1}{2}\)years 2 years 3\(\frac{1}{2}\)years Ans . 1
Q.30 A sum of money amounts to ₹850 in 3 years and to ₹925 in 4 years at some rate of simple interest. The sum is : ₹550 ₹600 ₹625 ₹700 Ans . 3
Q.31 In what time will 1,860 amount to ₹2,641.20 at simple interest 12% per annum ? 3 years 3\(\frac{1}{2}\)years 4 years 4\(\frac{1}{2}\) years Ans . 2
Q.32 The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10,000, the present population is 4600 6400 7600 6000 Ans . 2
Q.33 The sum lent at 5% per annum (i.e. 365 days) simple interest, that produces interest, of ₹2.00 a day, is ₹1400 ₹14700 ₹14600 ₹7300 Ans . 3
Q.34 A certain sum of money lent out at simple interest amounts to ₹1380 in 3 years and ₹1500 in 5 years. Find the rate per cent per annum. 3% 3.5% 4% 5% Ans . 3
Q.35 If a sum of money amounts to ₹12,900 and ₹14,250 at the end of 4th year and 5th year respectively at a certain rate of simple interest, then the rate of interest is 10% 12% 18% 20% Ans . 3
Q.36 In what time will ₹8,000, at 3% per annum, produce the same interest as ₹6, 000 does in 5 years at 4 % simple interest ? 5 years 6 years 3 years 4 years Ans . 1
Q.37 The principal which gives ₹1 interest per day at a rate of 5% simple interest per annum is ₹5000 ₹7300 ₹36500 ₹3650 Ans . 2
Q.38 A sum of money lent out at simple interest amounts to ₹720 after 2 years and Rs. 1020 after a further period of 5 years. Find the principal. ₹600 ₹1740 ₹6000 ₹120 Ans . 1
Q.39 The simple interest on Rs. 36,000 for the period from 5th January to 31st May, 2013 at 9.5% per annum is Rs. 1,338 Rs. 1425 Rs. 1400 Rs. 1368 Ans . 4
Q.40 Alipta got some amount of money from her father. In how many years will the ratio of the money and the interest obtained from it be 10:3 at the rate of 6% simple interest per annum? 7 years 3 years 5 years 4 years Ans . 3
Q.41 The sum of money that will yield Rs. 60 as simple interest at the rate of 6% per annum in 5 years 200 225 175 300 Ans . 1
Q.42 If a sum of money becomes Rs. 4000 in 2 years and Rs. 5500 in 4 years 6 months at the same rate of simple interest per annum, then the rate of simple interest is 21\(\frac{3}{7}\)% 21\(\frac{2}{7}\)% 21\(\frac{1}{7}\)% 21\(\frac{5}{7}\)% Ans . 1
Q.43 The simple interest on a certain sum of money at the rate of 5% per annum for 8 years is Rs. 840. Rate of interest for which the same amount of interest can be received on the same sum after 5 years is : 7% per annum 8% per annum 9% per annum 10% per annum Ans . 2
Q.44 A sum of Rs. 2800 is divided into two parts in such a way that the interest on both the parts is equal. If the first part is lent at 9% p.a. for 5 years and second part is for 6 years at 10% p.a., find the two sums. Rs. 1800, Rs. 1000 Rs. 1600, Rs. 1200 Rs. 1400, Rs. 1400 Rs. 1300, Rs. 1500 Ans . 2
Q.45 The simple interest on a sum for 5 years is two-fifth of the sum. The rate of interest per annum is 0.1 0.08 0.06 0.04 Ans . 2
Q.46 If the simple interest on Rs. 400 for 10 years is Rs. 280, the rate of interest per annum is 7% 7\(\frac{1}{2}\)% 7\(\frac{1}{4}\)% 8\(\frac{1}{2}\)% Ans . 1
Q.47 If the simple interest on Re. 1 for 1 month is 1 paisa, then the rate per cent per annum will be 10% 8% 12% 6% Ans . 3
Q.48 How much simple interest will Rs. 4000 earn in 18 months at 12% per annum? Rs. 216 Rs. 360 Rs. 720 Rs. 960 Ans . 3
Q.49 In how many years a sum of Rs. 3000 will yield an interest of Rs. 1080 at 12% per annum simple interest ? 4 years 3 years 5 years 2\(\frac{1}{2}\) years Ans . 2
Q.50 In simple interest rate per annum a certain sum amounts to Rs. 5,182 in 2 years and Rs. 5,832 in 3 years. The principal in rupees is Rs.2882 Rs.5000 Rs.3882 Rs.4000 Ans . 3
Q.51 For what sum will the simple interest at R% per annum for 2 years will be R ? Rs.\(\frac{100}{2R}\) Rs.50 Rs.\(\frac{100}{R}\) Rs.\(\frac{200}{R}\) Ans . 2
Q.52 The amount to be paid, when principal = Rs. 2000, rate of simple interest (R) = 5%, T = 2 years, is : Rs.3200 Rs.2400 Rs.2200 Rs.3400 Ans . 3
Q.53 The rate of simple interest for which Rs. 6,000 will amount to Rs. 6,900 in 3 years is 5% 7% 2% 4% Ans . 1
TYPE - IIQ.1 A sum of money becomes \( \frac{7}{6} \) of itself in 3 years at a certain rate of simple interest. The rate per annum is : \( 5\frac{5}{9} \)% \( 6\frac{5}{9}\)% 18% 25% Ans . 1
Q.2 A sum of money becomes \( \frac{41}{40} \) of itself in \( \frac{1}{4} \)years at a certain rate of simple interest. The rate of interest per annum is 10% 1% 2.5% 5% Ans . 1
Q.3 A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest ? 8 years 10 years 12 years 14 years Ans . 2
Q.4 At what rate per cent per annum will the simple interest on a sum of money be \( \frac{2}{5} \) of the amount in 10 years ? 4% 6% 5\(\frac{2}{3}\)% 6\(\frac{2}{3}\)% Ans . 4
Q.5 ₹6,000 becomes ₹7,200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be ₹8000 ₹8250 ₹9250 ₹9000
Ans . 2
Q.6 A sum of money at simple interest trebles itself in 15 years. It will become 5 times of itself in 40 years 36 years 30 years 25 years Ans . 3
Q.7 If a sum of money at simple interest doubles in 12 years, the rate of interest per annum is 16\(\frac{2}{3}\)% 7.5% 8\(\frac{1}{3}\)% 10% Ans . 3
Q.8 At what rate of simple interest per annum will a sum become \( \frac{7}{4} \) of itself in 4 years ? 18% 18 \( \frac{1}{4} \) 18 \( \frac{3}{4} \)% 18 \( \frac{1}{2} \)% Ans . 3
Q.9 A sum of money at a certain rate per annum of simple interest doubles in the 5 years and at a different rate becomes three times in 12 years. The lower rate of interest per annum is 15% 20% 15\(\frac{3}{4}\)% 16\( \frac{2}{3} \)% Ans . 4
Q.10 In how many years will a sum of money double itself at 6\(\frac{1}{4}\)% simple interest per annum ? 24 years 20 years 16 years 12 years Ans . 3
Q.11 At a certain rate of simple interest, a certain sum of money becomes double of itself in 10 years. It will become treble of itself in 15 years 18 years 20 years 30 years Ans . 3
Q.12 In how much time, will a sum of money become double of itself at 15% per annum simple interest? 6\(\frac{1}{4}\) years 6\(\frac{1}{2}\) years 6\(\frac{1}{3}\) years 6\(\frac{2}{3}\) years Ans . 4
Q.13 In how many years will a sum of money double itself at 12% per annum? 8 yrs. 6 months 6 yrs. 9 months 8 yrs. 4 months 7 yrs. 4 months Ans . 3
Q.14 A sum amounts to double in 8 years by simple interest. Then the rate of simple interest per annum is 10% 12.5% 15% 20% Ans . 2
Q.15 A sum doubles itself in 16 years, then in how many years will it triple itself; rate of interest being simple 25 years 32 years 48 years 64 years Ans . 2
Q.16 In certain years a sum of money is doubled to itself at 6\(\frac{1}{4}\)% simple interest per annum, then the required time will be 16 years 12\(\frac{1}{2}\) years 8 years 10\(\frac{2}{3}\) years Ans . 1
Q.17 The simple interest on a sum of money is \( \frac{8}{25} \) of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annumis 5 8 6\(\frac{1}{4}\) 4 Ans . 2
Q.18 A certain sum doubles in 7 years at simple interest. The same sum under the same interest rate will become 4 times in how many years. 14 28 21 10 Ans . 3
Q.19 A certain sum of money amounts to Rs. 2200 at 5% p.a. rate of interest, Rs. 2320 at 8% interest in the same period of time. The period of time is 3 years 4 years 5 years 2 years Ans . 4
Q.20 At what per cent of simple interest will a sum of money double itself in 15 years? 6\( \frac{1}{3}\)% 6\( \frac{2}{3}\)% 6\( \frac{1}{2}\)% 6% Ans . 2
Q.21 If a sum of money deposited in a bank at simple interest is doubled in 6 years, then after 12 years, the amount will be \( \frac{5}{2} \) times the original ammount 3 times the original ammount \( \frac{7}{2} \) times the original ammount 4 times the original ammount Ans . 2
Q.22 The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is : 30% 40% 50% 55% Ans . 3
Q.23 If a sum of money doubles itself in 8 years, then the interest rate in percentage is 8\(\frac{1}{2}\)% 10% 10\(\frac{1}{2}\)% 12\(\frac{1}{2}\)% Ans . 4
Q.24 The rate of simple intereset per annum at which a sum of money doubles itself in 16\(\frac{2}{3}\)years is 4% 5% 6% 6\(\frac{2}{3}\)% Ans . 3
TYPE - IIIQ.1 In what time will the simple interest be \(\frac{2}{5}\) of the principal at 8 per cent per annum? 8 years 7 years 5 years 6 years Ans . 3
Q.2 The simple interest on a sum after 4 years is \(\frac{1}{5}\) of the sum. The rate of interest per annum is 4% 5% 6% 8% Ans . 2
Q.3 Simple interest on a certain sum for 6 years is \( \frac{9}{25} \) of the sum. The rate of interest is 6% 6\(\frac{1}{2}\)% 8% 8\(\frac{1}{2}\)% Ans . 1
Q.4 The simple interest on a sum for 5 years is one fourth of the sum. The rate of interest per annum is 5% 6% 4% 8% Ans . 1
Q.5 On a certain sum, the simple interest at the end of 6\(\frac{1}{4}\) years becomes \(\frac{3}{8}\) of the sum. The rate of interest is 5% 6% 7% 8% Ans . 2
Q.6 The present worth of a bill due 7 months hence is Rs.1200 and if the bill were due at the end of 2\(\frac{1}{2}\) years its present worth would be Rs.1016. The rate per cent is 5% 10% 15% 20% Ans . 2
Q.7 At the rate of simple interest per annum, the interest on a certain sum of money for 10 years will be \(\frac{2}{5}\)th part of the amount, then the rate of simple interest is 5% 6\(\frac{2}{3}\)% 7% 4\(\frac{1}{2}\)% Ans . 2
Q.8 A and B borrowed Rs. 3000 and Rs. 3200 respectively at the same rate of interest for 2\(\frac{1}{2}\) years. If B paid Rs. 40 more interest than A, find the rate of interest. 5% 7% 8% 6% Ans . 3
TYPE-IVQ.1 The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by ₹42. The sum is : ₹210 ₹280 ₹750 ₹840 Ans . 4
Q.2 The difference between the simple interest received from two different sources on ₹1500 for 3 years is ₹13.50. The difference between their rates of interest is: 0.1% 0.2% 0.3% 0.4% Ans . 3
Q.3 The simple interest on a sum of money is \(\frac{4}{9}\) of the principal and the number of years is equal to the rate percent per annum. The rate per annum is : 5% \(6\frac{2}{3}\)% 6% \(7\frac{1}{5}\)% Ans . 2
Q.4 The simple interest on a certain sum for 8 months at 4% per annum is ₹129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is : ₹2580 ₹2400 ₹2529 ₹3600 Ans . 4
Q.5 Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ? ₹1700 ₹1800 ₹1900 ₹2000 Ans . 4
Q.6 Simple interest on a certain sum at a certain annual rate of interest is \( \frac{16}{25} \) of the sum. If the number representing rate per cent and time in years be equal, then the rate of interest is 8% \(11\frac{1}{2}\)% \(12\frac{1}{2}\)% \(12\frac{1}{4}\)% Ans . 1
Q.7 A sum of ₹1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is : ₹500 ₹1000 ₹750 ₹1250 Ans . 3
Q.8 If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after 20 years 30 years 10 years 22 years Ans . 1
Q.9 Simple interest on ₹500 for 4 years at 6.25% per annum is equal to the simple interest on ₹400 at 5% per annum for a certain period of time. The period of time is 4 years 5 years \(6\frac{1}{4}\) years \(8\frac{2}{3}\) years Ans . 3
Q.10 The simple interest on a sum of money is \( \frac{1}{16} \)of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is \(1\frac{1}{2} \)% \(2\frac{1}{2} \)% \(3\frac{1}{2} \)% \(4\frac{1}{2} \)% Ans . 2
Q.11 If ₹12,000 is divided into two parts such that the simple interest on the first part for 3 years at 12% per annum is equal to the simple interest on the second part for 4\(\frac{1}{2}\) years at 16% per annum, the greater part is ₹8000 ₹6000 ₹7000 ₹7500 Ans . 1
Q.12 The simple interest on a sum of money is \( \frac{1}{4} \) th of the principal and the number of years is equal to rate per cent per annum. The rate per cent is 2.5% 5% 7.5% 10% Ans . 2
Q.13 Equal sum of money are lent to X and Y at 7.5% per annum for a period of 4 years and 5 years respectively. If the difference in interest, paid by them was ₹150, the sum lent to each was ₹500 ₹1000 ₹2000 ₹3000 Ans . 3
Q.14 A sum of ₹1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part (In rupees) is 60 65 70 40 Ans . 1
Q.15 A borrows ₹800 at the rate of 12% per annum simple interest and B borrows ₹910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal ? 18 years 20 years 22 years 24 years Ans . 3
Q.16 The simple interest on a sum of money is \(\frac{1}{9}\) of the principal and the number of years is equal to rate per cent per annum. The rate per annum is 3% \(\frac{1}{3}\)% 3\(\frac{1}{3}\)% \(\frac{3}{10}\)% Ans . 3
Q.17 A person deposited ₹500 for 4 years and ₹600 for 3 years at the same rate of simple interest in a bank. Altogether he received ₹190 as interest. The rate of simple interest per annum was 4% 5% 2% 3% Ans . 2
Q.18 The difference between the simple interest received from two different banks on ₹500 for 2 years is ₹2.50. The difference between their (per annum) rate of interest is : 0.10% 0.25% 0.50% 1.00% Ans . 2
Q.19 In how many years will the simple interest on a sum of money be equal to the principal at the rate of 16\(\frac{2}{3}\)% per annum ? 4 years 5 years 6 years 8 yearss Ans . 3
Q.20 The rate of interest per annum at which the total simple interest of a certain capital for 1 year is equal to the total simple interest of the same capital at the rate of 5% per annum for 2 years, is \(\frac{5}{2}\)% 10% 25% 12.5% Ans . 2
Q.21 The simple interest on ₹4,000 in 3 years at the rate of x% per annum equals the simple interest on ₹5,000 at the rate of 12% per annum in 2 years. The value of x is 10% 6% 8% 9% Ans . 1
Q.22 If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interset on y for the same time and at the same rate of interest, then we have z2 = xy xyz = 1 x2 = yz y2= zx Ans . 4
Q.23 Prakash lends a part of ₹20,000 at 8% simple interest and remaining at \(\frac{4}{3}\)% simple interest. His total income after a year was ₹800. Find the sum lent at 8%. ₹8000 ₹12000 ₹6000 ₹10000 Ans . 1
Q.24 Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amount in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is ₹1350, then the sum deposited in each case is : ₹3000 ₹4000 ₹5000 ₹6500 Ans . 3
Q.25 The difference between simple interest and the true discount on Rs. 2400 due 4 years hence at 5% per annum simple interest is Rs.30 Rs.70 Rs.80 Rs.50 Ans . 3
TYPE-VQ.1 A sum of ₹1550 was lent partly at 5% and partly at 8% simple interest. The total interest received after 3 years is ₹300. The ratio of money lent at 5% to that at 8% is : 5 : 8 8 : 5 31 : 6 16 : 15 Ans . 4
Q.2 A person lent ₹5,000 partly at the rate of 4 per cent and partly at the rate of 5 per cent per annum simple interest. The total interest after 2 years is ₹440. To find the sum of money lent at each of the above rates, ₹5,000 is to be divided in the ratio : 4 : 5 3 : 2 5 : 4 2 : 3 Ans . 2
Q.3 A person borrows some money for 5 years and loan amount : total interest amount is 5 : 2. The ratio of loan amount : interest rate is equal to : 2 : 25 2:1 5:2 25:2 Ans . 4
Q.4 A person invests money in three different schemes for 6 years, 10 years and 12 years at 10 per cent, 12 per cent and 15 per cent simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is 6:3:2 2:3:4 3:4:6 3:4:2 Ans . 1
Q.5 With a given rate of simple inerest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is 4% 6% 5% 7% Ans . 3
Q.6 Ratio of the principal and the amount after 1 year is 10:12. Then the rate of interest per annum is : 12% 16% 18% 20% Ans . 4
Q.7 In a certain time, the ratio of a certain principal and the simple interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years the money was invested is 1 year 3 years 5 years 7 years Ans . 2
Q.8 ₹12,000 is divided into two parts so that the simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for 4\(\frac{1}{2}\) years at 16% per annum. The ratio of the first part to the second part is 2:1 1:2 2:3 3:2 Ans . 1
Q.9 If ratio of principal and simple interest for 1 year is 25 : 1, then the rate of interest is 4% 25% 5% 20% Ans . 1
Q.10 If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is : 5% 6% 8% 3% Ans . 2
Q.11 A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is Rs.2900 Rs.2200 Rs.2400 Rs.3100 Ans . 3
TYPE-VIQ.1 A sum of ₹400 amounts to ₹480 in 4 years. What will it amount to if the rate of interest is increased by 2%? ₹484 ₹560 ₹512 None of these Ans . 3
Q.2 A man loses ₹55.50 yearly when the annual rate of interest falls from 11.5% to 10%. His capital (in rupees) is 3700 7400 3325 11100 Ans . 1
Q.3 If the annual rate of simple interest increases from 10% to 12 \(\frac{1}{2}\)% , a man’s yearly income increases by ₹1250. His principal (in rupees) is 50000 45000 60000 65000 Ans . 1
Q.4 A sum was invested on simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched ₹72 more. The sum is ₹1200 ₹1500 ₹1600 ₹1800 Ans . 1
Q.5 A sum of money was lent at simple interest at a certain rate for 3 years. Had it been lent at 2.5% per annum higher rate, it would have fetched ₹540 more. The money lent was : ₹6400 ₹6472 ₹6840 ₹7200 Ans . 4
Q.6 A sum of money was invested at a certain rate of simple interest for 2 years . Had it been invested at 1% higher rate, it would have fetched ₹24 more i nterest. The sum of money is : ₹1200 ₹1050 ₹1000 ₹9600 Ans . 1
Q.7 A person who pays income tax at the rate of 4 paise per rupee, find that a fall of interest rate from 4% to 3.75% diminishes his net yearly income by ₹48. What is his capital ? ₹24000 ₹25000 ₹20000 ₹18000 Ans . 3
Q.8 A sum was lent at simple interest at a certain rate for 2 years. Had it been lent at 3% higher rate, it would have fetched ₹300 more. The original sum of money was : ₹5000 ₹6000 ₹7000 ₹4000 Ans . 1
Q.9 A sum of ₹2,400 amounts to ₹3,264 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 1%, the same sum in the same time would amount to ₹3288 ₹3312 ₹3340 ₹3360 Ans . 4
Q.10 ₹800 amounts to ₹920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to ₹1056 ₹1112 ₹1182 ₹992 Ans . 4
Q.11 A sum of Rs. 800 amounts to Rs. 920 in 3 years at the simple interest rate. If the rate is increased by 3% p.a., what will be the sum amount to in the same period ? ₹992 ₹962 ₹942 ₹982 Ans . 1
Q.12 The amount ₹2,100 became ₹2,352 in 2 years at simple interest. If the interest rate is decreased by 1%, what is the new interest ? ₹210 ₹220 ₹242 ₹252 Ans . 1
Q.13 A sum of Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will the same sum become in 3 years ? Rs.1025 Rs.1042 Rs.1052 Rs.1024 Ans . 3
Q.14 The rate of simple interest per annum of bank being decreased from 5% to 3\(\frac{1}{2}\) %, the annual income of a person from interest was less by Rs. 105. The sum deposited at the bank was Rs.6000 Rs.7200 Rs.6800 Rs.7000 Ans . 4
TYPE-VIIQ.1 A sum of ₹10,000 is lent partly at 8% and remaining at 10% per annum. If the yearly interest on the average is 9.2%, the two parts are : ₹4000,₹6000 ₹4500,₹5500 ₹5000,₹5000 ₹5500,₹4500 Ans . 1
Q.2 A sum of ₹1000 is lent out partly at 8% and the remaining at 10% per annum. If the yearly income on the average is 9.2%, the two parts respectively are ₹400,₹600 ₹450,₹550 ₹500,₹500 ₹550,₹450 Ans . 1
Q.3 An old article is available for 12,000 at cash payment or is available for ₹7,000 cash payment and a monthly instalment of ₹630 for 8 months. The rate per cent per annum is 2.1% 3% 3.25% 3.3% Ans . 1
Q.4 The effective annual rate of interest, corresponding to a nominal rate of 6% per annum payable half yearly, is : 6.06% 6.07% 6.08% 6.09% Ans . 4
Q.5 A person lends 40% of his sum of money at 15% per annum, 50% of rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum ? 13.4% 14.33% 14.4% 13.33% Ans . 3
Q.6 Ramesh deposited ₹15600 in a fixed deposit at the rate of 10% per annum simple interest. After every second year, he adds his interest earnings to the principal. The interest at the end of fourth year is ₹1716 ₹1560 ₹3432 ₹1872 Ans . 4
Q.7 A part of ₹1500 was lent at 10% per annum and the rest at 7% per annum simple interest. The total interest earned in three years was ₹396. The sum lent at 10% was ₹900 ₹800 ₹700 ₹600 Ans . 1
Q.8 What equal instalment of annual payment will discharge a debt which is due as ₹848 at the end of 4 years at 4% per annum simple interest ? ₹212 ₹200 ₹250 ₹225 Ans . 2
Q.9 Out of ₹50,000, that a man has, he lends ₹8000 at 5\( \frac{1}{2} \)% per annum simple interest and Rs. 24,000 at 6 % per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of ₹3680. The rate of interest per annum, at which the remaining money is lent, is 5% 7% 10% 12% Ans . 3
Q.10 A man invests half his capital at the rate of 10% per annum, onethird at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets, is 9% 10% 10.5% 12% Ans . 2
Q.11 John invested a sum of money at an annual simple interest rate of 10%. At the end of four years the amount invested plus interest earned was ₹770. The amount invested was ₹650 ₹350 ₹550 ₹500 Ans . 3
Q.12 Arun lends ₹20,000 to two of his friends. He gives ₹12,000 to the first at 8% p.a. simple interest. Arun wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is 8% 16% 12% 13% Ans . 4
Q.13 A person invests ₹12,000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs he has to withdraw the entire money after 3 years, for which the bank allowed him a lower rate of interest. If he gets ₹3,320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is \( 7\frac{5}{9} \)% \( 7\frac{4}{9} \)% \( 7\frac{8}{9} \)% \( 8\frac{7}{9} \)% Ans . 2
Q.14 A certain scheme of investment in simple interest declares that it trebles the investment in 8 years. If you want to quadruple your money through that scheme, you have to invest it for : 11 years 6 months 10 years 8 months 10 years 12 years Ans . 4
Q.15 If a man receives on one-fourth of his capital 3% interest, on two third 5% and on the remainder 11%, the percentage he receives on the whole is 4.5% 5% 5.5% 5.2% Ans . 2
Q.16 At the same rate of simple interest sum of the interest of ₹300 for 4 years and the interest of ₹400 for 3 years is ₹120. The rate of interest is 5% 4% 6% 10% Ans . 1
Q.17 Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is ₹8,160, the money borrowed by him (in ₹) was 12000 6000 8000 10000 Ans . 3
Q.18 Two equal sums were lent out at 7% and 5% S.I. respectively. The interest earned on the two loans add up to ₹960 for 4 years. The total sum lent out in ₹3500 ₹2500 ₹2000 ₹3000 Ans . 3
Q.19 Mohan lends Rs. 500 to John and a certain sum to Tom at the same time at a simple interest of 8% per annum. If in 4 years, he altogether receives Rs. 210 as interest from the two, then the sum of money he lent to Tom was Rs.144.75 Rs.148 Rs.156.25 Rs.165.50 Ans . 3
Q.20 What should be the least number of years in which the simple interest on Rs. 2600 at 6\(\frac{2}{3}\) % will be an exact number of rupees ? 3 2 5 4 Ans . 1
Q.21 Ram bought a bike for Rs. 60,000. He paid Rs. 10000 cash down and the rest at the end of 2 years at 15% simple interest. How much more did he pay as simple interest ? Rs.15000 Rs.25000 Rs.35000 Rs.50000 Ans . 1
Q.22 A sum of Rs. 7,930 is divided into three parts and given on loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then A received a loan of Rs.3050 Rs.2760 Rs.2750 Rs.2800 Ans . 2
Q.23 A man buys a TV priced at Rs. 16000. He pays Rs. 4000 at once and the rest after 15 months on which he is charged a simple interest at the rate of 12% per year. The total amount he pays for the TV is Rs.18200 Rs.17800 Rs.16800 Rs.17200 Ans . 2
Q.24 If Rahim deposited the same amount of Rs. x in a bank at the beginning of successive 3 years and the bank pays simple interest of 5% per annum, then the amount at his credit at the end of 3rd year will be : Rs. \( \frac{861x}{400} \) Rs. \( \frac{1261x}{400} \) Rs. \( \frac{21x}{20} \) Rs. \( \frac{25241x}{8000} \) Ans . 4
Q.25 A boy aged 12 years is left with Rs. 100,000 which is under a trust. The trustees invest the money at 6% per annum and pay the minor boy a sum of Rs. 2500, for his pocket money at the end of each year. The expenses of trust come out to be Rs. 500 per annum. Find the amount that will be handed over to the minor boy after he attains the age of 18 years. Rs.120000 Rs.150000 Rs.118000 Rs.125000 Ans . 3
Q.26 If A borrowed Rs. P at x% and B borrowed Rs. Q (> P) at y% per annum at simple interest at the same time, then the amount of their debts will be equal after 100 \( (\frac{Q-P}{Px-Qy}) \) years 100 \( (\frac{Px-Qy}{Q-P}) \) years 100 \( (\frac{Px-Qy}{P-Q}) \) years 100 \( (\frac{P-Q}{Px-Qy}) \) years Ans . 1
Q.27 A money lender claims to lend money at the rate of 10% per annum simple interest. However, he takes the interest in advance when he lends a sum for one year. At what interest rate does he lend the money actually? 10% 10\(\frac{1}{9}\)% 11% 11\(\frac{1}{9}\)% Ans . 4
Q.28 Ramesh borrowed a sum at 5 per annum simple interest from Rahul. He returns the amount after 5years. Rahul returns 2 % of the total amount received. How much did Ramesh borrowed if he received Rs. 5? Rs.250 Rs.200 Rs.150 Rs.175 Ans . 2
Q.29 A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest be 10% per annum, then how much profit or loss will he have? Rs.55 gain Rs.30 profit Rs.30 loss Rs.30 profit Ans . 1
Q.30 A money lender lends Rs. 400 for 3 years to a person and lends Rs. 500 for 4 years to the other person at the same rate of simple interest. If altogether he receives Rs. 160 as interest, what is the rate of interest per annum ? 5% 7% 9% 10% Ans . 1
TEST YOURSELFQ.1 A Co-operative Bank gives H.B. loans under the condition that if the loan be cleared with interest in five years, the rate of simple interest per year is 5%, otherwise it will be 7%. Mr. Rahim and Mr. Ram take the same amount of H.B. loan and clear the loan with interest in 5 and 8 years respectively. If Ram pays Rs. 62,000 more, what is the amount of loan taken by each of them ? Rs.200000 Rs.180000 Rs.190000 Rs.210000 Ans . 1
Q.2 A person on retirement gets Rs. 3,20,000 from his gratuity and P.F. He wants to invest this amount in Post Office and Bank in such a way that he earns a total interest of Rs. 27,600 every year. If the annual rate of interest in Post Office and Bank be respectively 9% and 8%, What are the amounts invested in Post Office and Bank respectively ? Rs.200000 , Rs.120000 Rs.180000 and Rs.140000 Rs.185000 , Rs.135000 None of these Ans . 1
Q.3 A person on retirement gets Rs. 3,20,000 from his gratuity and P.F. He wants to invest this amount in Post Office and Bank in such a way that he earns a total interest of Rs. 27,600 every year. If the annual rate of interest in Post Office and Bank be respectively 9% and 8%, What are the amounts invested in Post Office and Bank respectively ? Rs.2500,Rs.4500 Rs.4000,Rs.6000 Rs.5000,Rs.7000 Rs.6000,Rs.8000 Ans . 3
Q.4 A person made a fixed deposit of Rs. 30,000 in a bank for 5 years at 10% simple interest per annum. He had to withdraw the whole amount after 3 years to meet the expenses of his daughter’s marriage and he received Rs. 7800 less than what he would have got after 5 years. What is the rate of simple interest per annum paid by the bank for this premature encashment ? 6% 7% 8% 9% Ans . 3
Q.5 In 4 years, ₹6000 amounts to ₹8,000. In what time at the same rate will ₹525 amount to ₹700 ? 5 years 3 years 4 years None of these Ans . 3
Q.6 Find the interest on ₹1460 at 10% from 5th February, 1992 to 25th April, 1992 ₹32 ₹36 ₹40 ₹34 Ans . 1
Q.7 Find the amount Ram will get after 2 years when he invests ₹15000 at 15% interest. ₹18500 ₹19500 ₹17500 ₹16500 Ans . 2
Q.8 At what rate per annum will a sum of ₹5000 amount to ₹6000 in 4 years? 6% per annum 4% per annum 5% per annum 4.5% per annum Ans . 3
Q.9 Ram lent ₹1200 to Shyam for 5 years and ₹1500 to Mohan for 2 years received altogether ₹900 as interest. Find the rate per annum. 8.5% 8% 9% 10% Ans . 4
Q.10 A certain sum of money amounts to Rs. 1680 in 3 years and to ₹1800 in 5 years. Find the sum and the rate of interest. ₹1500;4% ₹1200;4% ₹1600;5% ₹1800;5% Ans . 1
Q.11 In how many years will a sum of money double itself at 5% rate of interest? 18 years 20 years 22 years 15 years Ans . 2
Q.12 A man lends a certain sum of money and gets an interest equal to \( \frac{1}{16} \)th of the principal. The time for which money was lent is equal to the rate of interest. Find the rate of interest per annum. 4% 3.5% 3% 2.5% Ans . 4
Q.13 A man borrowed ₹16000 from two persons. He paid 6% interest to one and 10% per annum to the other. In one year he paid total interest 1120. How much did he borrow at each rate? ₹10000 ; ₹6000 ₹12000 ; ₹4000 ₹11000 ; ₹5000 ₹12500 ; ₹3500
Ans . 2
Q.14 A borrowed ₹1500 at 4% per annum and ₹1400 at 5% per annum for the same period. He paid ₹390 as total interest. Find the time for which he borrowed the sum. 3.5 years 2.5 years 3 years 4 years Ans . 3
Q.15 Find the annual instalment that will discharge a debt of ₹12900 due in 4 years at 5% per annum simple interest. ₹2750 ₹2150 ₹2500 ₹3000 Ans . 4
Q.16 A certain sum of money amounts to ₹6780 in 2 years and to ₹7360.50 in 3\(\frac{1}{2}\) years. Find the sum and the rate of interest. ₹6006 ; 6.4 % per annum ₹8006 ; 6.4 % per annum ₹5006 ; 5% per annum ₹5506 ; 5% per annum Ans . 1
Q.17 If 5600 amounts to 6678 in 3\(\frac{1}{2}\) years, what will 9600 amount to in 5\(\frac{1}{4}\) years at the same rate of interest ? ₹12732 ₹12372 ₹12722 ₹12237 Ans . 2
Q.18 A man promises to his wife a birthday present, given her each year a number of rupees equal to the number of years in her age. If her birthday falls on August 8, what sum must be placed at simple interest at 7% on January 1 before she is 63 (non leap year) in order to raise the required sum ? ₹1600 ₹1550 ₹1500 ₹1450 Ans . 3
Q.19 It is decided that a loan of ₹10,000 will be paid off at the rate of ₹800 per month in 15 equal instalments. Find out the rate of return on investment. 17% P.a. 18% P.a. 15% P.a. 16% P.a. Ans . 4
Q.20 A person takes loan of ₹4,000 on the condition that he would pay it in the monthly instalment of ₹500. He has to pay interest @ 6% on the outstanding balances, then find out the average rate of interest received by the creditor. \(3\frac{3}{8}\)% per annum \(2\frac{3}{8}\)% per annum \(4\frac{3}{8}\)% per annum \(3\frac{1}{8}\)% per annum Ans . 1
Q.21 Divide 6800 into two parts so that S.I. on the first part for 3 \(\frac{1}{3}\) years at 6% may be equal to the interest on the second part for 3\(\frac{1}{2}\) years at 4% Percent Per annum ₹2600;₹4200 ₹2800;₹4000 ₹2500;₹4300 ₹2700;₹4100 Ans . 2
At what rate of simple interest will a sum of money doubles itself in 25 2 years?Detailed Solution
The Sum of money doubles itself in 25 years. Concept: Simple interest is the interest calculated on the principal portion of the loan or the original contribution to the saving account. ∴ The rate of interest per annum is 4%.
In what time will the simple interest on a certain sum of money at 7.5% per annum be 3/8 of itself?⇒ T = 10 years.
In what time will the simple interest on a certain sum of money at 61 4 Pa be 3/8 of itself?∴Rate(R)=100×IP×T=100×3x8x×254=100×32×25=6% Q. The simple interest on a certain sum of money is 38th of the sum in 614 years.
In what time will the simple interest on a certain sum of money at 6 1 2 per annum be 3/8th of itself?⇒T=6 years.
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In what time will the simple interest on a certain sum of money at 25 2 )% per annum be 3/8 of itself?
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