Interest - Aptitude MCQ Questions and Solutions with Explanations

11

A person invests Rs. 12000 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 three years, for which the bank allowed him a lower rate of interest. If he gets Rs. 3320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is = ?

A) $${\text{7}}\frac{5}{9}$$ % B) $${\text{7}}\frac{4}{9}$$ % C) $${\text{7}}\frac{8}{9}$$ % D) $${\text{8}}\frac{7}{9}$$ %

Discuss

Answer & Solution

Answer: Option B

Solution:

Principal = Rs. 12000
Rate % = 10%
Interest paid by the person in 5 years
$$\eqalign{ & = \frac{{12000 \times 10 \times 5}}{{100}} \cr & = {\text{Rs}}{\text{. 6000}} \cr} $$
Interest received by the person after 3 years
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {6000 - 3320} \right) \cr & = {\text{Rs}}{\text{. 2680}} \cr & {\text{By using formula,}} \cr & {\text{Rate}}\% \cr & {\text{ = }}\frac{{2680}}{{12000}} \times \frac{{100}}{3} \cr & = \frac{{67}}{9} \cr & = 7\frac{4}{9}\% \cr & {\text{Hence required rate}}\% \cr & {\text{ = 7}}\frac{4}{9}\% \cr} $$

12

A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?

A) 11 years 6 months B) 10 years 8 months C) 10 years D) 12 years

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{P}} + \frac{{P \times {\text{r}} \times {\text{t}}}}{{100}} = 3{\text{P}} \cr & \Rightarrow 1 + \frac{{rt}}{{100}} = 3 \cr & \Rightarrow \frac{{{\text{rt}}}}{{100}} = 2 \cr & \Rightarrow {\text{r}} = \frac{{2 \times 100}}{8} = 25\% \cr & {\text{so, }}\,\left( {1 + \frac{{{\text{rt}}}}{{100}}} \right) = 4 \cr & \Rightarrow \frac{{{\text{rt}}}}{{100}} = 3 \cr & \Rightarrow {\text{t}} = \frac{{3 \times 100}}{{25}} \cr & \Rightarrow {\text{t}} = 12\,{\text{years}} \cr} $$

13

A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?

A) 4% B) 5% C) 2% D) 3%

Discuss

Answer & Solution

Answer: Option B

Solution:

Let rate of interest = R%
According to the question,
$$\eqalign{ & \frac{{500 \times 4 \times {\text{R}}}}{{100}} + \frac{{600 \times 3 \times {\text{R}}}}{{100}} = 190 \cr & \Rightarrow 20{\text{R + 18R = 190}} \cr & \Rightarrow 38{\text{R = 190}} \cr & \Rightarrow {\text{R = 5% }} \cr} $$
Hence required rate % = 5%

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let rate of interest = 1%
$$\eqalign{ & {\text{Case (I): Interest (}}{{\text{I}}_1}{\text{)}} \cr & {\text{ = }}\frac{{500 \times 4 \times 1}}{{100}} \cr & = 20 \cr & {\text{Case (II): Interest (}}{{\text{I}}_2}{\text{)}} \cr & {\text{ = }}\frac{{{\text{600}} \times 3 \times 1}}{{100}} \cr & = 18 \cr} $$
According to the question,

Interest	Rate %
38	1
↓×5	↓×5
190	5%

Hence required rate % = 5%

14

If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after

A) 10 years B) 20 years C) 22 years D) 30 years

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = 30\% \,{\text{of}}\,{\text{Rs}}{\text{.}}\,x \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{3x}}{{10}} \cr & {\text{Time}} = 6\,{\text{years}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 3x}}{{10 \times x \times 6}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr & {\text{Now, sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. }}x \cr & {\text{Rate}} = 5\% \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\,{\text{years}} \cr} $$

15

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%

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr} $$

16

If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then what is the relation between x, y, z we have = ?

A) x² = xy B) xyz = 1 C) x² = yz D) y² = zx

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the time is 't' years and the rate of interest is R%
According to the question,
$$\eqalign{ & {\bf{Case(I):}} \cr & y = \frac{{x \times {\text{R}} \times {\text{t}}}}{{100}}.....(i) \cr & {\bf{Case(II):}} \cr & z = \frac{{y \times {\text{R}} \times {\text{t}}}}{{100}}.....(ii) \cr} $$
By dividing equation (i) by equation (ii)
$$\eqalign{ & \frac{y}{z} = \frac{{x \times {\text{R}} \times {\text{t}}}}{{y \times {\text{R}} \times {\text{t}}}} \cr & \Rightarrow {y^2} = zx \cr} $$

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 Rs. 8160, the money borrowed by him (in Rupees) was?

A) Rs. 12000 B) Rs. 6000 C) Rs. 8000 D) Rs. 10000

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the money borrowed by Nitin = Rs. P
According to the question,
$$\eqalign{ & \frac{{{\text{P}} \times 6 \times 3}}{{100}} + \frac{{{\text{P}} \times 9 \times 5}}{{100}} + \frac{{{\text{P}} \times 13 \times 3}}{{100}} = {\text{Rs}}{\text{. }}8160 \cr & \Rightarrow \frac{{{\text{18P}}}}{{100}} + \frac{{{\text{45P}}}}{{100}} + \frac{{{\text{39P}}}}{{100}} = {\text{Rs}}{\text{. 1860}} \cr & \Rightarrow \frac{{{\text{102P}}}}{{100}} = {\text{Rs}}{\text{. 8160}} \cr & \Rightarrow {\text{P = Rs}}{\text{.}}\frac{{8160 \times 100}}{{102}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 8000}} \cr} $$

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let principal = Rs. 100
Total Interest
$$\frac{{100 \times 6 \times 3}}{{100}} + \frac{{100 \times 9 \times 5}}{{100}} + $$ $$\frac{{100 \times 13 \times 3}}{{100}}$$
$$\eqalign{ & = 18 + 45 + 39 \cr & = 102{\text{ units}} \cr & {\text{According to the question,}} \cr & {\text{102 units = Rs}}{\text{. 8160}} \cr & {\text{1 unit = Rs}}{\text{. }}\frac{{8160}}{{102}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 80}} \cr & {\text{100 units = Rs}}{\text{. 8000}} \cr & {\text{Hence sum = Rs}}{\text{. 8000}} \cr} $$

Alternate
Total rate of interest in 11 years
$$\eqalign{ & \left( {6 \times 3} \right)\% + \left( {5 \times 9} \right)\% + \left( {3 \times 13} \right)\% {\text{ }} \cr & \Rightarrow 102\% = 8160 \cr & \Rightarrow 100\% = 8000 \cr & \therefore {\text{Sum = Rs}}{\text{. 8000}} \cr} $$

18

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

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Increased interest in 3 years}} \cr & {\text{ = 3}} \times {\text{3}} \cr & {\text{ = 9% }} \cr & {\text{Hence increased amount}} \cr & {\text{ = }}\frac{{800 \times 9}}{{100}} \cr & = {\text{Rs}}{\text{. }}72 \cr & {\text{Total amount}} \cr & {\text{ = }}\left( {920 + 72} \right) \cr & = {\text{Rs}}{\text{. }}992 \cr} $$

19

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

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{sum}} = x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{\text{9}}}{{{\text{16}}}}x \cr & {\text{Let rate}} = {\text{R}}\% \,\text{and} \cr & \text{time} = R\,\text{years} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{{9x}}{{16}} \cr & \Rightarrow {{\text{R}}^2} = \frac{{900}}{{16}} \cr & {\text{R}} = \frac{{30}}{4} = 7\frac{1}{2} \cr & {\text{Hence,}} \cr & {\text{time}} = 7\frac{1}{2}\text{years} \cr} $$

20

A lends Rs. 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is :

A) Rs. 700 B) Rs. 1500 C) Rs. 4000 D) Rs. 6500

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the sum lent to C be Rs. x.
Then,
$$\eqalign{ & \left( {\frac{{2500 \times 7 \times 4}}{{100}}} \right) + \left( {\frac{{x \times 7 \times 4}}{{100}}} \right) = 1120 \cr & \Rightarrow \frac{{7x}}{{25}} = \left( {1120 - 700} \right) \cr & \Rightarrow x = \left( {\frac{{420 \times 25}}{7}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 1500. \cr} $$