Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & \frac{{\left( {n - 1} \right)}}{{{t_1}}} = \frac{{\left( {m - 1} \right)}}{{{t_2}}} \cr & \frac{1}{7} = \frac{3}{{{t_2}}} \cr & {t_2} = 21{\text{ years}} \cr} $$

$$\eqalign{ & {\text{Let sum = }}x \cr & {\text{Interest = }}\frac{3}{4}x{\text{ }} \cr & {\text{Interest = }}\frac{{{\text{PTR }}}}{{100}} \cr & \Rightarrow \frac{3}{4}x = \frac{{x \times {\text{R}} \times 12.5}}{{100}} \cr & {\text{R = 6}}\% \cr} $$

$$\eqalign{ & {\text{t}} = {\text{1 month = }}\frac{1}{{12}}{\text{year}} \cr & {\text{SI = 1 paisa = Rs}}{\text{. }}\frac{1}{{100}} \cr & {\text{r}}\% = \frac{{{\text{SI}} \times {\text{100}}}}{{{\text{P}} \times {\text{T}}}} = \frac{{1 \times 100 \times 12}}{{100 \times 1 \times 1}} \cr & {\text{r}}\% = 12\% \cr} $$

Let the three amounts be Rs. x, Rs. y and Rs. z,
Then,
$$\eqalign{ & \frac{{x \times 10 \times 6}}{{100}} = \frac{{y \times 12 \times 10}}{{100}} = \frac{{z \times 15 \times 12}}{{100}} \cr & \Rightarrow 60x = 120y = 180z \cr & \Rightarrow x = 2y = 3z = k(say) \cr & \Rightarrow x = k,y = \frac{k}{2},z = \frac{k}{3} \cr & \Rightarrow x:y:z = k:\frac{k}{2}:\frac{k}{3} \cr & \Rightarrow x:y:z = 1:\frac{1}{2}:\frac{1}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6:3:2 \cr} $$

Let total capital be Rs. x
Then,
  $$ \Rightarrow \left( {\frac{x}{3} \times \frac{7}{{100}} \times 1} \right) + \left( {\frac{x}{4} \times \frac{8}{{100}} \times 1} \right) + $$       $$\left( {\frac{{5x}}{{12}} \times \frac{{10}}{{100}} \times 1} \right)$$    $$ = 561$$
$$\eqalign{ & \Rightarrow \frac{{7x}}{{300}} + \frac{x}{{50}} + \frac{x}{{24}} = 561 \cr & \Rightarrow 51x = \left( {561 \times 600} \right) \cr & \Rightarrow x = \left( {\frac{{561 \times 600}}{{51}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6600 \cr} $$

$$\eqalign{ & {\text{Rate of interest}} = {\text{5}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr & {\text{sum}} = {\text{Rs}}{\text{. 3200}} \cr & {\text{Time}} = {\text{2 years 6 months}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\frac{1}{2}{\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{2}{\text{years}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{{\text{Prinicipal}} \times {\text{Time}} \times {\text{Rate}}}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\, = \frac{{3200 \times 5 \times 5}}{{2 \times 100}} \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr & \therefore {\text{Amount}} = {\text{Rs}}{\text{. sum}} + {\text{S}}{\text{.I}}. \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {3200 + 400} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 3600}}{\text{}} \cr} $$

$$\eqalign{ & {\bf{Case - I:}} \cr & {\text{SI}}\% = {\text{R}}\% \times {\text{t}} \cr & {\text{SI}}\% = {\text{5}}\% \times {\text{8}} \cr & = {\text{40}}\% \cr & {\bf{Case - II:}} \cr & {\text{SI}}\% = {\text{5}} \times {\text{r}}\% {\text{ }} \cr & {\text{According to the question}} \cr & \Rightarrow {\text{40}}\% = {\text{5}} \times {\text{r}}\% \cr & \Rightarrow {\text{r}}\% = {\text{8}}\% \cr} $$

Money is double itself means interest is equal to money.
$$\eqalign{ & {\text{P = }}\frac{{{\text{P}} \times {\text{8}} \times {\text{r}}}}{{100}} \cr & \Rightarrow {\text{r = }}\frac{{100}}{8} \cr & \Rightarrow {\text{r = 12}}\frac{1}{2}\% \cr} $$

$$\eqalign{ & {\text{Let principal and SI is}} \cr & {\text{ = }}10x,{\text{ }}3x{\text{ }} \cr & {\text{and time is = }}t \cr & \Rightarrow 3x = \frac{{10x \times 6 \times t}}{{100}} \cr & \Rightarrow t = 5\,{\text{years}} \cr} $$

$$\eqalign{ & {\text{By using formula }} \cr & \Leftrightarrow \frac{{{\text{3000}} \times 12 \times {\text{T}}}}{{100}} = 1080 \cr & \Leftrightarrow {\text{T = }}\frac{{108}}{{36}}{\text{ = 3 years}} \cr} $$