Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Principal = Rs 8000}} \cr & {\text{Amount = Rs 8820}} \cr & {\text{Let Rate = }}R \cr & {\text{Time = 2 years}} \cr & {\text{By using formula, }} \cr & \Rightarrow 8820 = 8000{\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \Rightarrow \frac{{8820}}{{8000}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \Rightarrow \frac{{441}}{{400}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & {\text{Taking square root of both sides,}} \cr & \Rightarrow \frac{{21}}{{20}} = \left( {1 + \frac{R}{{100}}} \right) \cr & \Rightarrow R = 5\% \cr} $$

$$\eqalign{ & {\text{Rate = 10}}\% \cr & {\text{Time = 2 years}} \cr & {\text{Effective rate of CI for 2 years}} \cr & {\text{ = 10 + 10 + }}\frac{{10 \times 10}}{{100}} \cr & = 21\% \cr & {\text{Effective rate of SI for 2 years}} \cr & {\text{ = 2}} \times {\text{10 = 20}}\% \cr & {\text{Required SI}} \cr & {\text{ = }}\frac{{420}}{{21}} \times {\text{20 = Rs. 400}} \cr} $$

x becomes 3x in 3 years
Therefore 3x also becomes 9x in 3 years
Required years = 3 + 3 = 6

Let the share of the younger and elder sons be Rs. x and Rs. (16400 - x)
Then, amount of Rs. x after 3 years = Amount of Rs. (16400 - x) after 2 years
$$\eqalign{ & \Rightarrow x{\left( {1 + \frac{5}{{100}}} \right)^3} = \left( {16400 - x} \right){\left( {1 + \frac{5}{{100}}} \right)^2} \cr & \Rightarrow x\left( {1 + \frac{5}{{100}}} \right) = \left( {16400 - x} \right) \cr & \Rightarrow \frac{{21x}}{{20}} + x = 16400 \cr & \Rightarrow \frac{{41x}}{{20}} = 16400 \cr & \Rightarrow x = \left( {\frac{{16400 \times 20}}{{41}}} \right) \cr & \Rightarrow x = 8000 \cr} $$

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. on Rs}}{\text{. 672 for 1 year}} \cr & {\text{ = Rs}}{\text{. }}\left( {714 - 672} \right) \cr & {\text{ = Rs}}{\text{. 42}} \cr & \therefore {\text{Rate = }}\left( {\frac{{100 \times 42}}{{672 \times 1}}} \right){\text{% }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 6}}{\text{.25% }} \cr} $$

Here, b – a = 3 – 2 = 1
B = Rs. 1728, A = Rs.1440
$$\eqalign{ & R\% = \left( {\frac{B}{A} - 1 \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{1728}}{{1440}} - 1 \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{288}}{{1440}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr} $$

$$\eqalign{ & {\text{Required rate }}\% \cr & {\text{ = }}\frac{{\left( {238.50 - 225} \right)}}{{225}} \times 100 \cr & = 6\,\% \cr} $$

$$\eqalign{ & {\text{Rate }} \Rightarrow {\text{ 10% = }}\frac{1}{{10}} \cr & {\text{Each installment of 2 years}} \cr & \Rightarrow \frac{{10}}{{11}} \times \frac{{\left( {10 + 11} \right)}}{{11}} \times {\text{ Installment = P}}{\text{.A}} \cr & {\text{P}}{\text{.A = 21000}} \cr & {\text{Each installment = 12100}} \cr} $$

S.I. on Rs. 4624 for 1 year
$$\eqalign{ & {\text{ = Rs. }}\left( {4913 - 4624} \right) \cr & {\text{ = Rs. 289}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 289}}{{4624 \times 1}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\frac{1}{4}\% \cr & {\text{Now,}} \cr & x{\left( {1 + \frac{{25}}{{400}}} \right)^2} = 4624 \cr & \Rightarrow x \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} = 4624 \cr & \Rightarrow x = \left( {4624 \times \frac{{16}}{{17}} \times \frac{{16}}{{17}}} \right) \cr & \Rightarrow x = 4096 \cr} $$

$$\eqalign{ & 12000 \times {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 24000 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^5} = 2 \cr & \therefore {\left[ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^5}} \right]^4} = {2^4} = 16 \cr & \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \cr & \Rightarrow {\text{P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}}{\text{ = 16P}} \cr & \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 16 \times 12000 \cr & \Rightarrow 12000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{20}} = 192000 \cr} $$