If a sum of money at simple interest doubles in 5 years it will become 4 times in how many years

Exercise 1

1. The rate at which a sum becomes four times of itself in 15 years at S.I., will be :

   	A.	15%
   	B.	$$17\frac{1}{2}\%$$
   	C.	20%
   	D.	25%

   Answer & Explanation

   Answer: Option C

   Explanation:

   Let sum = x Then, S.I. = 3x

   $$\therefore$$ Rate = ($$\frac{100 * S.I}{P * T}$$)

   = ($$\frac{100 * 3x}{x * 15}$$)%

   = 20%.

2. If a sum of money at simple interest doubles in 6 years, it will become 4 times in :

   	A.	12 years
   	B.	14 years
   	C.	16 years
   	D.	18 years

   Answer & Explanation

   Answer: Option D

   Explanation:

   Let sum = x. Then, S.I. = x.

   $$\therefore$$ Rate = ($$\frac{100 * x}{x * 6}$$)%

   = $$\frac{50}{3}\%$$.

   Now, sum = x, S.I. = 3x, Rate = $$\frac{50}{3}\%$$.

   Time = $$\frac{100 * 3x}{x * \frac{50}{3}}$$ = 18 years.

3. A sum of money trebles itself in 15 years 6 months. In how many years would it double itself ?

   	A.	6 years 3 months
   	B.	7 years 9 months
   	C.	8 years 3 months
   	D.	9 years 6 months

   Answer & Explanation

   Answer: Option B

   Explanation:

   Let sum = x Then, S.I. = 2x.

   Time = 15$$\frac{1}{2}$$years = $$\frac{31}{2}$$years.

   $$\therefore$$ Rate = ($$\frac{100 * 2x}{x * \frac{31}{2}}$$)%.

   = $$\frac{400}{31}\%$$

   Now, sum = x, S.I. = x, Rate = $$\frac{400}{31}\%$$.

   Time = $$\frac{100 * x}{x * \frac{400}{31}}$$

   = $$\frac{31}{4}$$years

   = 7 years 9 months.

4. The simple interest on a sum of money at 8% per annum for 6 ears is half the sum. The sum is :

   	A.	Rs. 4800
   	B.	Rs. 6000
   	C.	Rs. 8000
   	D.	Data inadequate

   Answer & Explanation

   Answer: Option D

   Explanation:

   Let sum = x. Then, S.I. = $$\frac{x}{2}$$.

   $$\therefore$$ $$\frac{x}{2}$$ = $$\frac{x * 8 * 6}{100}$$ Clearly, data is inadequate.

5. Consider the, following statements :

   If a sum of money is lent at simple interest, then the

   1. money gets doubled in 5 years if the rate of interest is $$16\frac{2}{3}\%$$.

   2. money gets doubled in 5 years if the rate of interest is 20%.

   3. money becomes four times in 10 years if it gets doubled in 5 years. Of these statements,

   	A.	1 and 3 are correct
   	B.	2 alone is correct
   	C.	3 alone is correct
   	D.	2 and 3 are correct

   Answer & Explanation

   Answer: Option B

   Explanation:

   Let Sum be x Then, S.I. = x.

   1.Time = $$\frac{100 * x}{x * \frac{50}{3}}$$ = 6 years (False)

   2.Time = $$\frac{100 * x}{x * 20}$$ = 5 years(True)

   3.Suppose sum = x.

   Then, S.I = x and Time = 5 years.

   Rate = ($$\frac{100 * x}{x * 5}$$)% = 20%.

   Now, sum = x, S.I. = 3x and Rate = 20%.

   $$\therefore$$ Time = ($$\frac{100 * 3x}{x * 20}$$)years = 15 years (False)

   So, 2 alone is correct.

6. At what rate percent per annum will the simple interest on a sum of money be $$\frac{2}{5}$$of the amount in 10 year ?

   	A.	4%
   	B.	$$5\frac{2}{3}\%$$
   	C.	6%
   	D.	$$6\frac{2}{3}\%$$

   Answer & Explanation

   Answer: Option A

   Explanation:

   Let sum = x. Then, S.I. = $$\frac{2x}{5}$$, Time = 10 years.

   $$\therefore$$ Rate = ($$\frac{100 * 2x}{x * 5 * 10}$$)% = 4%.

7. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum ?

   	A.	$$1\frac{1}{4}$$ years
   	B.	$$1\frac{3}{4}$$ years
   	C.	$$2\frac{1}{4}$$ years
   	D.	$$2\frac{3}{4}$$ years

   Answer & Explanation

   Answer: Option A

   Explanation:

   Let sum = x Then, S.I. = 0.125x = $$\frac{1}{8}$$x, R = 10%.

   Time = ($$\frac{100 * x}{x * 8 * 10}$$)years

   = $$\frac{5}{4}$$years

   = 1$$\frac{1}{4}$$years.

8. How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 40% ?

   	A.	5 years
   	B.	6 years
   	C.	7 years
   	D.	8 years

   Answer & Explanation

   Answer: Option D

   Explanation:

   Let the sum be x. Then, S.I. = 40% of x = $$\frac{2x}{5}$$; Rate = 5%.

   $$\therefore$$ Time = (100 * $$\frac{2x}{5}$$ * $$\frac{1}{x * 5}$$) = 8 years.

9. 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 :

   	A.	$$5\frac{5}{9}\%$$
   	B.	$$6\frac{5}{9}\%$$
   	C.	18%
   	D.	25%

   Answer & Explanation

   Answer: Option A

   Explanation:

   Let sum = x Then, amount = $$\frac{7x}{6}$$.

   S.I. = ($$\frac{7x}{6}$$ - x) = $$\frac{x}{6}$$; Time = 3 years.

   $$\therefore$$ Rate = ($$\frac{100 * x}{x * 6 * 3}$$)%

   = $$\frac{50}{9}\%$$

   = 5$$\frac{5}{9}\%$$

10. Simple interest on a certain sum at a certain annual rate of interest is $$\frac{1}{9}$$ of the sum.If the numbers representing rate percent and time in years be equal, then the rate of interest is :

    	A.	$$3\frac{1}{3}\%$$
    	B.	5%
    	C.	$$6\frac{2}{3}\%$$
    	D.	10%

    Answer & Explanation

    Answer: Option A

    Explanation:

    Let sum = x. Then, S.I. = $$\frac{x}{9}$$.

    Let rate = R% and time = R years.

    $$\therefore$$ ($$\frac{x * R * R}{100}$$) = $$\frac{x}{9}$$

    <=> R2 = $$\frac{100}{9}$$

    <=> R = $$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

    Hence, rate =3$$\frac{1}{3}\%$$.