Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{C}}{\text{.I}}{\text{.}}\, = Rs.\,\left[ {4000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 4000} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {4000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} - 4000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,840 \cr & \therefore {\text{Sum}} = Rs.\,\left( {\frac{{420 \times 100}}{{3 \times 8}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1750 \cr} $$

$$\eqalign{ & {\text{Sum}} = Rs.\,\left( {\frac{{50 \times 100}}{{2 \times 5}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,500 \cr & {\text{Amount}} = Rs.\,\left[ {500 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {500 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,551.25 \cr & \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left( {551.25 - 500} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,51.25 \cr} $$

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}}\, = Rs.\,\left( {\frac{{1200 \times 5 \times 2}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr & {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left[ {1200 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1200} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,123 \cr & \therefore {\text{Difference}} = Rs.\,\left( {123 - 120} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3 \cr} $$

$$\left[ {15000 \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - 15000} \right]$$       $$ - $$ $$\left( {\frac{{15000 \times R \times 2}}{{100}}} \right)$$    $$ = 96$$
$$ \Rightarrow 15000\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^2} - 1 - \frac{{2R}}{{100}}} \right] = 96$$
$$ \Rightarrow 15000$$  $$\left[ {\frac{{{{\left( {100 + R} \right)}^2} - 10000 - \left( {200 \times R} \right)}}{{10000}}} \right]$$       $$ = 96$$
$$\eqalign{ & \Rightarrow {R^2} = {\frac{{96 \times 2}}{3}} = 64 \cr & \Rightarrow R = 8 \cr & \therefore {\text{Rate}} = 8\% \cr} $$

$$\eqalign{ & \text{Let the sum be Rs. P} \cr & \text{Then, }\, {P{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - P} = 525 \cr & \Rightarrow P\left[ {{{\left( {\frac{{11}}{{10}}} \right)}^2} - 1} \right] = 525 \cr & \Rightarrow P = {\frac{{525 \times 100}}{{21}}} = 2500 \cr & \therefore \text{Sum} = Rs.\,2500 \cr & \text{So, S.I.} = Rs.\left( {\frac{{2500 \times 5 \times 4}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,500 \cr} $$

$$\eqalign{ & {\text{Principal = Rs. 2000}} \cr & {\text{Amount = Rs. 2420}} \cr & {\text{Rate = 10% }} \cr & {\text{By using formula,}} \cr & \Rightarrow 2420 = 2000{\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{2420}}{{2000}} = {\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{121}}{{100}} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow {\left( {\frac{{11}}{{10}}} \right)^2} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow n = 2 \cr & {\text{Hence,}} \cr & {\text{required time = 2 years}} \cr} $$

Alternative
Note : In such type of questions to save your valuable time follow the given below method.

		Principal	:	Amount
Ratio	→	2000	:	2420
		100	:	121

$${\text{Rate = 10% = }}\frac{1}{{10}}$$

		Principal	:	Amount
1st year	→	10	:	11
2nd year	→	10	:	11
Ratio	→	100	:	121

Note : Now after 2nd year both the principal and amount will be in the same ratio.
Hence required time = 2 years

Note : In such type of questions to save your valuable time follow the given below method
Rate % = 5%
Effective Rate of CI for 3 years = 15.7625%
Effective Rate of SI for 3 years = 5 × 3 = 15%

According to the question
$$\eqalign{ & \left( {15.7625 - 15} \right)\% \,{\text{of sum}} {\text{ = Rs. 36}}{\text{.60}} \cr & {\text{0}}{\text{.7625% of sum}} {\text{ = Rs. 36}}{\text{.60}} \cr & {\text{Sum = }}\frac{{36.60}}{{0.7625}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}4800 \cr} $$

$$\eqalign{ & {\text{Amount}} \cr & {\text{ = Rs}}{\text{.}}\left[ {8400 \times {{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^3}} \right] \cr & = {\text{Rs}}{\text{.}}\left( {8400 \times \frac{9}{8} \times \frac{9}{8} \times \frac{9}{8}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{382725}}{{32}}} \right) \cr & = {\text{Rs}}.11960.156 \approx {\text{Rs}}.11960.16 \cr & {\text{C}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {11960.16 - 8400} \right) \cr & = {\text{Rs}}{\text{.}}\,3560.16 \cr} $$

$$\eqalign{ & {\text{Let Principal = P}} \cr & {\text{Rate = R% }} \cr & {\text{T = 4 years}} \cr & \therefore {\text{Amount = 2P}} \cr & {\text{Case (I) 2P = P}}{\left( {1 + \frac{R}{{100}}} \right)^4} \cr & 2 = {\left( {1 + \frac{R}{{100}}} \right)^4}.....(i) \cr & {\text{Case (II) Let after t years it will be 8 times}} \cr & {\text{8P = P}}{\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\left( 2 \right)^3} = {\left( {1 + \frac{R}{{100}}} \right)^t}.....(ii) \cr & {\text{By using equation (i) & equation (ii)}} \cr & {\left( {1 + \frac{R}{{100}}} \right)^{12}} = {\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\text{By comparing both sides,}} \cr & {\text{t = 12 years}} \cr} $$

Let the sum be Rs. x
$$\eqalign{ & \therefore 1352 = x{\left( {1 + \frac{4}{{100}}} \right)^2} \cr & \Rightarrow 1352 = x{\left( {1 + \frac{1}{{25}}} \right)^2} \cr & \Rightarrow 1352 = x{\left( {\frac{{26}}{{25}}} \right)^2} \cr & \Rightarrow x = \frac{{1352 \times 25 \times 25}}{{26 \times 26}} \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,1250 \cr} $$