Interest - Aptitude MCQ Questions and Solutions with Explanations

71

Veena obtained an amount of Rs. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. what is the amount invested by veena?

A) Rs. 16660 B) Rs. 17180 C) Rs. 17450 D) Rs. 18110 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{8376}} \cr & {\text{R}} = 8\% \cr & {\text{T}} = {\text{6}}{\kern 1pt} {\text{years}} \cr & \therefore {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 8376}}{{8 \times 6}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}17450 \cr} $$

72

At which sum the simple interest at the rate of $$3\frac{3}{4}$$ % per annum will be Rs. 210 in $$2\frac{1}{3}$$ years?

A) Rs. 1580 B) Rs. 2400 C) Rs. 2800 D) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 210}} \cr & {\text{R}} = 3\frac{3}{4}\% = \frac{{15}}{4}\% \cr & {\text{T}} = {\text{2}}\frac{{\text{1}}}{{\text{3}}}{\text{years}} = \frac{7}{3}{\text{years}} \cr & \therefore {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210}}{{\frac{{15}}{4} \times \frac{7}{3}}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210 \times 4 \times 3}}{{15 \times 7}}} \right) \cr & = {\text{Rs}}{\text{. }}2400 \cr} $$

73

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

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

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let principal = 10P}} \cr & {\text{Interest = 10P}} \times \frac{{30}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 3P}} \cr & {\text{According to the question,}} \cr & {\text{Case (I)}} \cr & \Rightarrow 3{\text{P = }}\frac{{{\text{10P}} \times {\text{R}} \times {\text{6}}}}{{100}} \cr & \Rightarrow {\text{R = 5}}\% \cr & {\text{Case (II)}} \cr & {\text{Interest = Principal = 10P}} \cr & \Rightarrow {\text{10P = }}\frac{{{\text{10P}} \times {\text{5}} \times {\text{t}}}}{{100}} \cr & \Rightarrow {\text{t = 20 years}} \cr} $$

74

A person invests money in three different schemes for 6 years, 10 years and 12 years at 10%, 12% and 15% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is = ?

A) 6 : 3 : 2 B) 2 : 3 : 4 C) 3 : 4 : 6 D) 3 : 4 : 2

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the principal in each case = 100 units According to the question,

		1^st part	2^nd part	3^rd part
Principal	→	100_x6	100_x3	100_x2
Rate %	→	10	12	15
Time	→	6	10	12
Interest	→	60_x6	120_x3	180_x2

Interest Interest is same in each, so equal the interest.
Hence required ratio
= 600 : 300 : 200 of sum
= 6 : 3 : 2

75

Rs. 1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 2000 after = ?

A) 15 years B) 18 years C) 20 years D) $$16\frac{2}{3}$$ years

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1000 }} \cr & {\text{Rate = 5}}\% \cr & {\text{Interest for first 10 years}} \cr & = \frac{{1000 \times 5 \times 10}}{{100}} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{After 10 years principal}} \cr & = {\text{(1000}} + {\text{500)}} \cr & {\text{ = Rs}}{\text{. 1500}} \cr & {\text{Remaining interest}} \cr & {\text{ = Rs}}{\text{. (2000}} - {\text{1500)}} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Required time }} \cr & {\text{ = }}\frac{{500}}{{1500}} \times \frac{{100}}{5} \cr & = \frac{{100}}{15} \cr & = \frac{{20}}{3} \cr & = 6\frac{2}{3}{\text{ years}} \cr & {\text{Total time}} \cr & = \left( {10 + 6\frac{2}{3}} \right){\text{years}} \cr & {\text{ = 16}}\frac{2}{3}{\text{ years}} \cr} $$

76

The simple interest at x% for x years will be Rs. x on a sum of:

A) Rs. x B) Rs. $$\frac{{100}}{x}$$ C) Rs. 100x D) Rs. $$\frac{{100}}{{{x^2}}}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Sum}} = {\frac{{100 \times S.I.}}{{R \times T}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100 \times x}}{{x \times x}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100}}{x}} \cr} $$

77

Rs. 6200 amounts to Rs. 9176 in 4 years at simple interest. If the interest rate is increased by 3% it would amount to how much?

A) Rs. 8432 B) Rs. 9820 C) Rs. 9920 D) Rs. 10920

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 6200}} \cr & {\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{9176}} - {\text{6200}}} \right) \cr & = {\text{Rs}}{\text{. }}2976 \cr & {\text{T}} = 4\,{\text{years}} \cr & \therefore {\text{Rate}} \cr & = \left( {\frac{{100 \times 2976}}{{6200 \times 4}}} \right)\% \cr & = 12\% \cr & {\text{New }}{\text{rate}} \cr & = \left( {12 + 3} \right)\% \cr & = 15\% \cr & {\text{New}}\,{\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{{\text{6200}} \times 15 \times 4}}{{100}}} \right) \cr & = \text{Rs.} \,3720 \cr & {\text{New}}\,{\text{amount}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{6200}} + 3720} \right) \cr & = {\text{Rs}}{\text{.}}\,9920 \cr} $$

78

The simple interest accrued on a certain principal in 5 years at the rate of 12 p.c.p.a. is Rs.1536. what amount of simple interest would one get if one invests Rs.1000 more than the previous principal for 2 years and at the same rate p.c.p.a. ?

A) Rs. 614.40 B) Rs. 845.40 C) Rs. 1536 D) Rs. 2136 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

$$\eqalign{ & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 1536}}{{12 \times 5}}} \right) \cr & = {\text{Rs}}{\text{. }}2560 \cr & Now, \cr & P = {\text{Rs}}{\text{.}}\left( {2560 + 1000} \right) \cr & \,\,\,\,\,\, = {\text{Rs}}{\text{. }}3560 \cr & {\text{T}} = {\text{2years}} \cr & {\text{R}} = {\text{12}}\% \cr & \therefore S.I. \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{3560 \times 12 \times 2}}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,854.40 \cr} $$

79

The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840. At what rate of interest the same account of interest can be received on the same sum after 5 years?

A) 6% B) 8% C) 9% D) 10%

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 840}} \cr & {\text{R}} = {\text{5}}\% \cr & {\text{T}} = 8\,{\text{years}} \cr & {\text{Principal}} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{100 \times 840}}{{5 \times 8}}} \right) \cr & = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{Now,}} \cr & {\text{P}} = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{840}} \cr & {\text{T}} = {\text{5 years}}{\text{}} \cr & \therefore {\text{Rate}} \cr & = \left( {\frac{{100 \times 840}}{{2100 \times 5}}} \right)\% \cr & = {\text{8}}\% \cr} $$

80

Rs. 6000 becomes Rs. 7200 in 4 years. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be = ?

A) Rs. 8000 B) Rs. 8250 C) Rs. 9250 D) Rs. 9000

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr & \underbrace {\,\,\,\,\,{\text{6000}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{7200}}\,\,\,\,\,}_{ + 1200} \cr & {\text{By using formula,}} \cr & {\text{Rate }}\% \cr & = \frac{{1200}}{{6000}} \times \frac{{100}}{4} \cr & {\text{ = 5}}\% \cr & {\text{New rate}}\% \cr & = {\text{5}} \times \frac{3}{2} = {\text{7}}{\text{.5}}\% \cr & {\text{Interest after 5 years}} \cr & = \frac{{6000 \times 7.5 \times 5}}{{100}} \cr & {\text{ = Rs}}{\text{. 2250}} \cr & {\text{Hence,}} \cr & {\text{amount }} \cr & {\text{ = Rs}}{\text{. }}\left( {6000 + 2250} \right) \cr & {\text{ = Rs 8250}} \cr} $$