Interest - Aptitude MCQ Questions and Solutions with Explanations

Let Sum = Rs. x. Then, S.I. = Rs. x, Time = 16 years
$$\eqalign{ & \therefore {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 16}}} \right)\% = {\frac{25}{4}}\% = {6\frac{1}{4}}\% \cr & {\text{Now, sum}} = {\text{Rs}}{\text{. }}x, \cr & {\text{Time}} = 8{\kern 1pt} {\text{years}} \cr & {\text{Rate}} = 6\frac{1}{4}\% \cr & \therefore {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{x \times 25 \times 8}}{{100 \times 4}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{2} \cr & {\text{So,}} \cr & {\text{Amount}} = {\text{Rs}}{\text{.}}\left( {x + \frac{x}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{{3x}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\frac{1}{2}{\text{ times}} \cr} $$

$$\eqalign{ & {\text{Let sum be x}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = x \cr & {\text{I - Time}} \cr & = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr & = 6\,{\text{years(false)}} \cr & {\text{II}} - {\text{Time}} \cr & = \frac{{100 \times x}}{{x \times 20}} \cr & = 5\,{\text{years(True)}} \cr & {\text{III}} - {\text{Suppose sum}} = x. \cr & {\text{Then, S}}{\text{.I}}{\text{. }} = x \cr & {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr & {\text{Now, sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr & {\text{So, B alone is correct}}{\text{.}} \cr} $$

According to the question,

Principal	Interest
10	3

$$\eqalign{ & {\text{Rate }}\% {\text{ = 10}}\% \cr & {\text{Time = }}\frac{3}{{10}} \times \frac{{100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 3\,{\text{years}} \cr} $$

Let the amount invested = Rs. P
According to the question,
$$\eqalign{ & {\text{P}} + \frac{{{\text{P}} \times 10 \times 4}}{{100}} = 770 \cr & \Rightarrow {\text{P}} + \frac{{4{\text{P}}}}{{10}} = 770 \cr & \Rightarrow \frac{{14{\text{P}}}}{{10}} = 770 \cr & \Rightarrow {\text{P}} = \frac{{770 \times 10}}{{14}} \cr & \Rightarrow {\text{P}} = {\text{Rs 550}} \cr} $$
Hence, required invested amount = Rs. 550

Alternate
$$\eqalign{ & {\text{10}}\% {\text{ = }}\frac{{1 \to {\text{Interest}}}}{{10 \to {\text{Principal}}}} \cr & {\text{Interest in 4 years}} \cr & {\text{ = 1}} \times {\text{4}} \cr & = {\text{4}} \cr & {\text{Amount = }} \cr & = \left( {{\text{Interest + Principal}}} \right) \cr & = 4 + 10 \cr & = 14 \cr & {\text{According to the question,}} \cr & {\text{14 units = 770}} \cr & {\text{1 unit = }}\frac{{770}}{{14}} \cr & {\text{10 units = }}\frac{{770}}{{14}} \times {\text{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 550 }} \cr & {\text{The amount invested}} \cr & {\text{ = Rs}}{\text{. 550}} \cr} $$

$$\eqalign{ & {\text{Rate }}\% = {\text{12}}\% \cr & {\text{Principal = Rs}}{\text{. 1860}} \cr & {\text{Amount = Rs}}{\text{. 2641}}{\text{.20}} \cr & {\text{Interest}} \cr & {\text{ = Rs}}{\text{. }}\left( {2641.20 - 1860} \right) \cr & = {\text{Rs}}{\text{. 781}}{\text{.20}} \cr & {\text{By using formula,}} \cr & {\text{Required time }} \cr & = \frac{{781.20 \times 100}}{{1860 \times 12}} \cr & = 3\frac{1}{2}{\text{ years}} \cr} $$

$$\eqalign{ & {\text{Let sum}} = x{\text{.}} \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{2} \cr & \therefore \frac{x}{2} = \frac{{x \times 8 \times 6}}{{100}} \cr} $$
Clearly, data is inadequate.

$$\eqalign{ & {\text{Let sum}} = x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = 0.125x = \frac{1}{8}x \cr & {\text{R}} = 10\% \cr & \therefore \text{Rate} \cr & = \left( {\frac{{100 \times x}}{{x \times 8 \times 10}}} \right){\text{years}} \cr & = \frac{5}{4}{\text{years}} \cr & = {\text{1}}\frac{1}{4}{\text{years}} \cr} $$

$$\eqalign{ & {\text{Present Population}} \cr & = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr & = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{4}{5}} \right)^2} \cr & = 10000 \times \frac{{16}}{{25}} \cr & = 400 \times 16 \cr & = 6400 \cr} $$

Let two parts are P₁ and P₂ respectively
According to the question
$$\eqalign{ & \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr & 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr & \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr & {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr & {\text{Hence,}} \cr & {\text{Required ratio = 2 : 1}} \cr} $$

Capital after paying income tax
$$\eqalign{ & \Rightarrow {\text{4}}\% - {\text{3}}{\text{.75}}\% = {\text{48}} \cr & \Rightarrow {\text{0}}{\text{.25}}\% {\text{ = 48}} \cr & {\text{100}}\% {\text{ = }}\frac{{48}}{{0.25}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19200 \cr} $$
⇒ Capital without paying income tax
⇒ 19200 = Capital × 96%
Net capital = 20000