Exercise 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%.
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.
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.
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.
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.
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%.
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.
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.
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$$\frac{5}{9}\%$$
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$$\frac{1}{3}\%$$.