Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 9534}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {{\text{11442}} - {\text{9534}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.1908}} \cr & {\text{R}} = {\text{4}}\% \cr & \therefore {\text{Time}} = \left( {\frac{{{\text{100}} \times {\text{1908}}}}{{{\text{9534}} \times {\text{4}}}}} \right){\text{years}} \cr & = \left( {\frac{{{\text{47700}}}}{{{\text{9534}}}}} \right){\text{years}} \approx {\text{5 years}} \cr} $$

$$\eqalign{ & {\text{Amount Rs 7000}} \cr & {\text{Total interest in 5 years}} \cr & {\text{ = 5}} \times \frac{{10}}{3}\% = \frac{{50}}{3}\% = \frac{1}{6} \cr} $$

Principal	Amount
6	(6 + 1)
↓ × 1000	↓ × 1000
6000	7000

Hence required principal = Rs. 6000

Let the amount invested = Rs. P
According to the questions,
$$\eqalign{ & \Leftrightarrow \frac{{{\text{P}} \times 9 \times {\text{2}}}}{{100}} + \frac{{{\text{P}} \times {\text{10}} \times {\text{2}}}}{{100}} = 760 \cr & \Leftrightarrow \frac{{ {18{\text{P + 20P}}} }}{{100}} = 760 \cr & \Leftrightarrow 38{\text{P = 76000}} \cr & \Leftrightarrow {\text{P = 2000}} \cr} $$

Alternate
Total interest percent
$$\eqalign{ & {\text{ = }}\left( {9 \times 2} \right)\% + \left( {10 \times 2} \right)\% \cr & \Rightarrow 38\% = 760 \cr & \Rightarrow 100\% = 2000 \cr} $$
Hence required principal
= Rs. 2000

$$\eqalign{ & {{\text{T}}_1} = 15\operatorname{months} \cr & \,\,\,\,\,\, = \frac{{15}}{{12}}years \cr & {R_1} = 7\frac{1}{2}\% = \frac{{15}}{2}\% \cr & {{\text{T}}_2} = 8\operatorname{months} \cr & \,\,\,\,\,\,\, = \frac{8}{{12}}years \cr & {{\text{R}}_2} = 12\frac{1}{2}\% = \frac{{25}}{2}\% \cr & {\text{Let the principal}} = {\text{P}} \cr & {\text{According to the question,}} \cr & \Leftrightarrow \frac{{{\text{P}} \times {\text{15}} \times {\text{15}}}}{{12 \times 2 \times 100}} - \frac{{{\text{P}} \times 25 \times 8}}{{12 \times 2 \times 100}} = 32.50 \cr & \Rightarrow \frac{{225{\text{P}}}}{{2400}} - \frac{{200{\text{P}}}}{{2400}} = 32.50 \cr & \Rightarrow \frac{{25{\text{P}}}}{{2400}} = 32.50 \cr & \Rightarrow {\text{P = Rs 3120}} \cr & {\text{Hence required principal}} \cr & {\text{ = Rs}}{\text{. 3120}} \cr} $$

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{.}}\,{\text{21250}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,\left( {{\text{26350}} - {\text{21250}}} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5100 \cr & {\text{T}} = {\text{6 years}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 5100}}{{{\text{21250}} \times {\text{6}}}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\% \cr} $$

$$\eqalign{ & {\text{P}} = {\text{Rs.}}{\text{ 8630}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs.}}{\text{ 1553}}{\text{.40}} \cr & {\text{T}} = {\text{3 years}} \cr & \therefore {\text{Rate}} \cr & = \left( {\frac{{100 \times 1553.40}}{{8630 \times 3}}} \right)\% \cr & = 6\% \cr} $$

$$\eqalign{ & {\text{Let the rate of be R}}\% {\text{p}}{\text{.a}}{\text{.}} \cr & Then, \cr & {\frac{{600 \times R \times 4}}{{100}}} + {\frac{{600 \times R \times 2}}{{100}}} = 180 \cr & \Rightarrow 2400{\text{R}} + 1200{\text{R}} = 18000 \cr & \Rightarrow 3600{\text{R}} = 18000 \cr & \Rightarrow {\text{R}} = 5\% \cr} $$

$$\eqalign{ & {\text{Let principal = P}} \cr & \therefore {\text{amount = 3P}} \cr & {\text{Interest = 3P}} - {\text{P}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 2P}} \cr & {\text{According to the question,}} \cr & {\text{2P = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{20}}}}{{100}} \cr & \Rightarrow {\text{R = 10% }} \cr} $$
Let after t years it will become double
$$\eqalign{ & {\text{Hence,}} \cr & {\text{Interest = 2P}} - {\text{P = P}} \cr & \Rightarrow {\text{P = }}\frac{{{\text{P}} \times 10 \times {\text{t}}}}{{100}} \cr & \Rightarrow {\text{t = 10 years}} \cr} $$

$$\eqalign{ & {\text{Loan Amount}}:{\text{Total Interest}} \cr & {\text{5}}:{\text{2}} \cr & {\text{Principal}} \to {\text{5}} \cr & {\text{Interest for 1 year}} \Rightarrow {\text{2}} \cr & {\text{Interest for 5 year}} \Rightarrow {\text{10}} \cr & {\text{10}} = \frac{{5 \times {\text{R}} \times 5}}{{100}} \cr & {\text{R}}\% = 40\% \cr & = \frac{{40}}{{100}} = \frac{2}{5} \cr & {\text{P}}:{\text{R}} = 5:\frac{2}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 25:2 \cr} $$

$$\eqalign{ & {\text{Half yearly rate}} \cr & {\text{ = }}\frac{6}{2} = 3\% \cr & {\text{Effective rate % }} \cr & {\text{ = 3}} + {\text{3}} + \frac{{3 \times 3}}{{100}} \cr & = 6.09\% \cr} $$