Practice MCQ Questions and Answer on Interest

71.

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is

(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700

Solution: $\begin{aligned} S .I . for 1 year \\ = Rs . (854 - 815) \\ = Rs .39 \\ S .I . for 3 years \\ = Rs . (39 \times 3) \\ = Rs . 117 \\ ∴ Principal \\ = Rs . (854 - 117) \\ = Rs . 698 \end{aligned}$

72.

A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is

(A) 4% p.a.
(B) 5% p.a.
(C) $6 \frac{1}{4}$ % p.a.
(D) $8 \frac{1}{3}$ % p.a.

Solution: Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a. Then, $\begin{aligned} 5000 \times R \times 4 = 4000 \times (R + 1) \times 4 \\ \Rightarrow \frac{R + 1}{R} = \frac{5000 \times 4}{4000 \times 4} \\ \Rightarrow 1 + \frac{1}{R} = 1 + \frac{1}{4} \\ \Rightarrow R = 4 \\ Hence, \\ Required rate = 4 % p .a . \end{aligned}$

73.

A sum of Rs. 10 is lent to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest is:

(A) $9 \frac{1}{11}$ %
(B) 10%
(C) 11%
(D) $21 \frac{9}{11}$ %

Solution: ⇒ Rs. 10 + S.I. on Rs. 10 for 11 months = Rs. 11 + S.I. on Rs. 1 for (1 + 2 + 3 + 4 + ........... + 10) months ⇒ Rs. 10 + S.I. on Rs. 1 for 110 months = Rs. 11 + S.I. on Rs. 1 for 55 months S.I. on Rs. 1 for 55 months = Rs. 1 $\begin{aligned} ∴ Rate = (\frac{100 \times 12}{1 \times 55}) % \\ = 21 \frac{9}{11} % \end{aligned}$

74.

A boy aged 12 years is left with Rs. 100000 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 ?

(A) Rs. 125000
(B) Rs. 118000
(C) Rs. 150000
(D) Rs. 120000

Solution: $\begin{aligned} Sum of the 12 years age \\ = Rs . 100000 \\ Sum of the 18 years age \\ = P + \frac{P \times R \times T}{100} \\ = 100000 + \frac{100000 \times 6 \times 6}{100} \\ = 100000 + 36000 \\ = 136000 \end{aligned}$ Total expenses = 2500 + 500 = 3000 per year Total expenses ( 6 years ) = 3000 × 6 = Rs. 18000 Amount obtained = 136000 - 18000 = 118000

75.

A man had 1000 hens at the beginning of year 2001 and the number of hens each year increases by 10% by giving birth. At the end of each year we double the no. of hens by purchasing the same no. of hens as there is the no. of hens with us at the time. What is the no. of hens at the beginning of 2004?

(A) 10600
(B) 10648
(C) 8848
(D) 8226

76.

A sum of Rs. 8,400 amounts to Rs. 11,046 at 8.75% p.a. simple interest in a certain time. What will be the simple interest (in Rs.) on a sum of Rs. 10,800 at the same rate for the same time?

(A) 3,204
(B) 3,024
(C) 3,402
(D) 3,420

Solution: $\begin{aligned} A = P + S .I . \\ S .I . = \frac{P \times R \times T}{100} \\ 11046 = 8400 + \frac{8400 \times 8.75 \times T}{100} \\ 2646 = \frac{84 \times 875 \times T}{100} \\ 2646 = 21 \times 35 \times T \\ T = 3.6 years \\ S .I . = \frac{10800 \times 8.75 \times 3.6}{100} \\ = \frac{108 \times 875 \times 36}{1000} \\ = 3402 \end{aligned}$

77.

A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?

(A) Rs. 400
(B) Rs. 500
(C) Rs. 700
(D) Rs. 800

Solution: Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y $\begin{aligned} Then, \\ \to 12 % of x + 10 % of y = 130 \\ \Rightarrow 12 x + 10 y = 13000 \\ \Rightarrow 6 x + 5 y = 6500. . . . . . (i) \\ And, \\ \to 10 % of x + 12 % of y = 134 \\ \Rightarrow 10 x + 12 y = 13400 \\ \Rightarrow 5 x + 6 y = 6700. . . . . . (ii) \\ Adding (i) and (ii), we get: \\ 11 (x + y) = 13200 \\ \Rightarrow x + y = 1200. . . . . . . (iii) \\ Subtracting (i) from (ii), \\ we get: - x + y = 200. . . . . . . (iv) \\ Adding (iii) and (iv), \\ we get : 2 y = 1400 o r y = 700 \\ Hence, \\ Amount invested at 12% \\ = (1200 - 700) \\ = Rs . 500 \end{aligned}$

78.

A man invested $\frac{1}{3}$ of his capital at 7%; $\frac{1}{4}$ at 8% and the remainder at 10%. If his annual income is Rs. 561, the capital is -

(A) Rs. 5400
(B) Rs. 6000
(C) Rs. 6600
(D) Rs. 7200

Solution: Let total capital be Rs. x Then, $\Rightarrow (\frac{x}{3} \times \frac{7}{100} \times 1) + (\frac{x}{4} \times \frac{8}{100} \times 1) +$ $(\frac{5 x}{12} \times \frac{10}{100} \times 1)$ $= 561$ $\begin{aligned} \Rightarrow \frac{7 x}{300} + \frac{x}{50} + \frac{x}{24} = 561 \\ \Rightarrow 51 x = (561 \times 600) \\ \Rightarrow x = (\frac{561 \times 600}{51}) \\ = 6600 \end{aligned}$

79.

Simple interest on a certain amount is $\frac{9}{16}$ of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is -

(A) $5 \frac{1}{2}$ years
(B) $6 \frac{1}{2}$ years
(C) 7 years
(D) $7 \frac{1}{2}$ years

Solution: $\begin{aligned} Let sum = x . \\ Then, \\ S .I . = \frac{9}{16} x \\ Let rate = R % and \\ time = R years \\ ∴ (\frac{x \times R \times R}{100}) = \frac{9 x}{16} \\ \Rightarrow R^{2} = \frac{900}{16} \\ R = \frac{30}{4} = 7 \frac{1}{2} \\ Hence, \\ time = 7 \frac{1}{2} years \end{aligned}$

80.

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 ?

(A) Rs. 1700
(B) Rs. 1800
(C) Rs. 1900
(D) Rs. 2000

Solution: Let the amount invested = Rs. P According to the questions, $\begin{aligned} \Leftrightarrow \frac{P \times 9 \times 2}{100} + \frac{P \times 10 \times 2}{100} = 760 \\ \Leftrightarrow \frac{18 P + 20P}{100} = 760 \\ \Leftrightarrow 38 P = 76000 \\ \Leftrightarrow P = 2000 \end{aligned}$ Alternate Total interest percent $\begin{aligned} = (9 \times 2) % + (10 \times 2) % \\ \Rightarrow 38 % = 760 \\ \Rightarrow 100 % = 2000 \end{aligned}$ Hence required principal = Rs. 2000

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Practice MCQ Questions and Answer on Interest

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