Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{A's,}}\,{\text{Principal}} = {\text{Rs}}{\text{. }}90,000 \cr & {\text{Rate}} = 5\% \cr & {\text{Time}} = 4{\text{ years}} \cr & \therefore {\text{S}}{\text{.I}} = \frac{{90,000 \times 5 \times 4}}{{100}} = {\text{Rs}}{\text{. }}18,000 \cr & {\text{B's,}}\,{\text{Principal}} = {\text{Rs}}{\text{. }}90,000 \cr & {\text{Rate}} = 7\% \cr & {\text{Time}} = 4{\text{ years}} \cr & \therefore {\text{S}}{\text{.I}} = \frac{{90,000 \times 7 \times 4}}{{100}} = {\text{Rs}}{\text{. }}25,200 \cr & \therefore {\text{Profit of A}} \cr & = \left( {25,200 - 18,000} \right) = {\text{Rs}}{\text{. }}7,200 \cr} $$

$$\eqalign{ & {\text{Amount after 3 years}} \cr & = 2000 + \frac{{2000 \times 5 \times 3}}{{100}} \cr & = 2000 + 300 \cr & = 2300 \cr & {\text{EMI}} = \frac{{A \times 100}}{{100 \times t + rt\left( {\frac{{t - 1}}{2}} \right)}} \cr & = \frac{{2300 \times 100}}{{100 \times 3 + 5 \times 3\left( {\frac{{3 - 1}}{2}} \right)}} \cr & = \frac{{2300 \times 100}}{{315}} \cr & = \frac{{2300 \times 20}}{{63}} \cr & = \frac{{46000}}{{63}} \cr & = 730\frac{{10}}{{63}} \cr} $$

$$\eqalign{ & {\text{Let, loan taken at rate of }}7\% = x \cr & {\text{Then, }}\frac{{\left( {2500 - x} \right) \times 5}}{{100}} + \frac{{x \times 7}}{{100}} = \frac{{276}}{2} \cr & 12500 - 5x + 7x = 13800 \cr & 2x = 13800 - 12500 \cr & 2x = 1300 \cr & x = 650\,{\text{Answer}} \cr} $$

$$\eqalign{ & {\text{Sum}} = 12,800 \cr & {{\text{I}}^{{\text{st}}}}{\text{ part}} = x \cr & {\text{I}}{{\text{I}}^{{\text{nd}}}}{\text{ part}} = \left( {12,800 - x} \right) \cr & x \times \frac{{15}}{{100}} + \left( {12,800 - x} \right)\frac{{12}}{{100}} = \frac{{5,085}}{3} \cr & \frac{{3x}}{{100}} + 128 \times 12 = 1,695 \cr & \frac{{3x}}{{100}} = 1,695 - 1,536 \cr & \frac{{3x}}{{100}} = 159 \cr & {\text{then }}x = 5,300 \cr} $$

$$\begin{array}{l}3\frac{4}{5}\text{yr}\stackrel{\text{S}\text{.I}}{\to }133\\ 1\text{yr}\stackrel{\text{S}\text{.I}}{\to }35\\ \text{If rate is double}\\ 1\text{yr}\stackrel{\text{S}\text{.I}}{\to }70\\ 5\text{yr}\stackrel{\text{S}\text{.I}}{\to }350\\ 420\stackrel{\text{Unit}}{\to }10500\\ 1\stackrel{\text{Unit}}{\to }25\\ 350\stackrel{\text{Unit}}{\to }350\times 25=8750\end{array}$$

$$\eqalign{ & {\bf{Given,}} \cr & {\text{Principal}} = {\text{Rs}}{\text{. }}10,000 \cr & {\text{Some part of money lent at }}15\% \cr & {\text{Some part of it lent at }}10\% \cr & {\text{Total interest earned}} = {\text{Rs}}{\text{. }}6,500 \cr & {\text{Time}} = 5{\text{ years}} \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{Interest}} = \frac{{{\text{Principal}} \times {\text{Rate}} \times {\text{Time}}}}{{100}} \cr & {\bf{Calculation:}} \cr & {\text{Let the money lent at }}15\% {\text{ be }}x \cr & {\text{Then money lent at }}10\% {\text{ be }}\left( {10,000 - x} \right) \cr & 6,500 = \frac{{x \times 15 \times 5}}{{100}} + \frac{{\left( {10,000 - x} \right) \times 10 \times 5}}{{100}} \cr & \Rightarrow 6,500 = \frac{{3x}}{4} + \frac{{10,000 - x}}{2} \cr & \Rightarrow 6,500 = \frac{{3x + 20,000 - 2x}}{4} \cr & \Rightarrow 26,000 = 20,000 + x \cr & \Rightarrow x = {\text{Rs}}{\text{. }}6,000 \cr & {\text{Then,}} \cr & \left( {10,000 - x} \right) = \left( {10,000 - 6,000} \right) = {\text{Rs}}{\text{. }}4000 \cr & {\text{Difference between the two sums lent}} \cr & = {\text{Rs}}{\text{. }}6,000 - {\text{Rs}}{\text{. }}4,000 \cr & = {\text{Rs}}{\text{. }}2,000 \cr & \therefore {\text{The difference between the sums lent is Rs}}{\text{. }}2,000 \cr} $$

\[\frac{1}{4}\begin{array}{*{20}{c}} {\,\,\,\, \leftarrow {\text{S}}{\text{.I}}{\text{.}}} \\ { \leftarrow P} \end{array}\]
$$\eqalign{ & {\text{Let }}P = 4x{\text{ and S}}{\text{.I}}{\text{.}} = x \cr & {\text{Time}} = t{\text{ years}} \cr & {\text{Rate}} = 4t\% \cr & \therefore {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times R \times T}}{{100}} \cr & x = \frac{{4x \times 4t \times t}}{{100}} \cr & {t^2} = \frac{{100}}{{16}} \cr & {t^2} = \frac{{25}}{4} \cr & \therefore t = \frac{5}{2} = 2.5{\text{ years}} \cr & \therefore R = 4 \times 2.5{\text{ years}} = 10\% \cr & {\text{New rate}} = 10\% + 2\% \cr & P = {\text{Rs}}{\text{. }}5000 \cr & T = 3{\text{ years}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times R \times T}}{{100}} \cr & = \frac{{5000 \times 12 \times 3}}{{100}} \cr & = {\text{Rs}}{\text{. }}1800 \cr} $$

Cash payment = 650000
Each installment = 25000
Total installment = 20
Sum = 25000 × 20 = 500000
Rate = 10% = $$\frac{1}{{10}}$$

⇒ Down payment = 650000 - 454545.45 = 195454.55 ≈ 195455

Difference between both part
$$\eqalign{ & = \left( {4 \times 15\% - 3 \times 20\% } \right){\text{ of }}8600 \cr & = 0\% {\text{ of }}8600 \cr & = 0{\text{ Answer}} \cr} $$