Practice MCQ Questions and Answer on Interest

101.

Consider the following statements
If a sum of money is lent at simple interest, then the
I - money gets doubled in 5 years if the rate of interest is $16 \frac{2}{3}$ %
II - money gets doubled in 5 years if the rate of interest is 20%.
III - money becomes four times in 10 years if it gets doubled in 5 years.

(A) I and III are correct
(B) II alone is correct
(C) III alone is correct
(D) II and III are correct

Solution: $\begin{aligned} Let sum be x . \\ Then, \\ S .I . = x \\ I - Time \\ = \frac{100 \times x}{x \times \frac{50}{3}} \\ = 6 years(false) \\ II - Time \\ = \frac{100 \times x}{x \times 20} \\ = 5 years(True) \\ III - Suppose sum = x . \\ Then, S .I . = x \\ Time = 5 years . \\ Rate = (\frac{100 \times x}{x \times 5}) % \\ = 20 % . \\ Now, sum = x, S .I . = 3 x and Rate = 20 % \\ ∴ Time = (\frac{100 \times 3 x}{x \times 20}) years \\ = 15 years (false) \\ So, B alone is correct . \end{aligned}$

102.

What sum will amount to Rs. 7000 in 5 years at $3 \frac{1}{3}$ % simple interest ?

(A) Rs. 6300
(B) Rs. 6500
(C) Rs. 6000
(D) Rs. 5000

Solution: $\begin{aligned} Amount Rs 7000 \\ Total interest in 5 years \\ = 5 \times \frac{10}{3} % = \frac{50}{3} % = \frac{1}{6} \end{aligned}$ Principal Amount 6 (6 + 1) ↓ × 1000 ↓ × 1000 6000 7000 Hence required principal = Rs. 6000

103.

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

104.

A milkman sells cow milk at the rate of Rs. 55 litre including a profit 12 per cent. He also sells buffalo milk at the rate of Rs. 36 per litre including a profit of 20%. How much profit will he earn in five days if he sells 8 litres of cow milk and 10 litres of buffalo milk per day?

(A) Rs. 632
(B) Rs. 624
(C) Rs. 646
(D) Rs. 642

Solution: Answer & Solution Answer: Option E Solution: $\begin{aligned} Total cow milksold in five days \\ = 5 \times 8 = 40 litres \\ Total buffalo milk sold in five days \\ = 5 \times 10 = 50 litres \\ Hence, \\ SP of 40 litres cow milk \\ = 40 \times 55 = R s . 2200 \\ Hence, \\ Profit on cow milk \\ = \frac{2200 \times 12}{112} = R s . 235.71 \\ Profit on buffalo milk \\ = \frac{50 \times 36 \times 20}{120} = R s . 300 \\ Thus, \\ Total Profit \\ = 235.71 + 300 = R s . 535.71 \end{aligned}$

105.

Deepak invested an amount of Rs. 21250 for 6 years. At what rate of simple interest will be obtain the total amount of Rs. 26350 at the end of 6 years?

(A) 5 p.c.p.a
(B) 6 p.c.p.a
(C) 8 p.c.p.a
(D) 12 p.c.p.a

Solution: Answer & Solution Answer: Option E Solution: $\begin{aligned} P = Rs . 21250 \\ S .I . = Rs . (26350 - 21250) \\ = Rs . 5100 \\ T = 6 years \\ ∴ Rate = (\frac{100 \times 5100}{21250 \times 6}) % \\ = 4 % \end{aligned}$

106.

If Rs. 12000 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 = ?

(A) Rs. 8000
(B) Rs. 6000
(C) Rs. 7000
(D) Rs. 7500

Solution: $\begin{aligned} Let the first part = Rs . x \\ ∴ Hence second part \\ = Rs . (12000 - x) \\ According to the question, \\ \Rightarrow \frac{x \times 12 \times 3}{100} = \frac{(12000 - x) \times 9 \times 16}{2 \times 100} \\ \Rightarrow 36 x = 72 (12000 - x) \\ \Rightarrow x = 24000 - 2 x \\ \Rightarrow 3 x = 24000 \\ \Rightarrow x = Rs . 8000 \\ 1^{st} part = Rs . 8000 \\ 2^{nd} part \\ = Rs . (12000 - 8000) \\ = Rs . 4000 \\ Hence maximum part \\ = Rs . 8000 \end{aligned}$ Alternate Note : In such type of questions to save your valuable time follow the given below method. Let two parts P1 and P2 respectively According to the question, $\begin{aligned} \Rightarrow P_{1} \times \frac{36}{100} \times 1 = P_{2} \times \frac{9}{2} \times \frac{16}{100} \times 1 \\ \Rightarrow P_{1} \times 4 = 8 P_{2} \\ \Rightarrow \frac{P_{1}}{P_{2}} = \frac{2}{1} \\ \Rightarrow P_{1} : P_{2} = 2 : 1 \\ Hence greater part \\ = \frac{12000}{(2 + 1)} \times 2 \\ = Rs . 8000 \end{aligned}$

107.

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 = ?

(A) 5%
(B) $6 \frac{2}{3}$ %
(C) 6%
(D) $7 \frac{1}{5}$ %

Solution: $\begin{aligned} Let the principal \\ = 9 units \\ Hence simple interest \\ = \frac{4}{9} \times 9 = 4 units \\ Let, \\ Rate of interest = R% \\ R = T (given) \\ By using formula \\ SI = \frac{P \times T \times R}{100} \\ 4 = \frac{9 \times R \times R}{100} \\ R^{2} = \frac{400}{9} \\ R = \frac{20}{3} = 6 \frac{2}{3} % \end{aligned}$

108.

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

109.

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

110.

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 ?

(A) Rs. 992
(B) Rs. 962
(C) Rs. 942
(D) Rs. 982

Solution: $\begin{aligned} Increased interest in 3 years \\ = 3 \times 3 \\ = 9% \\ Hence increased amount \\ = \frac{800 \times 9}{100} \\ = Rs . 72 \\ Total amount \\ = (920 + 72) \\ = Rs . 992 \end{aligned}$

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Practice MCQ Questions and Answer on Interest

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