Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & 9/8 \cr & {\text{Principle}} = 8{\text{ unit}} \cr & {\text{Amount}} = 9{\text{ unit}} \cr & {\text{Interest}} = 9.8{\text{ unit}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{8 \times 5 \times R}}{{100}} \cr & 1 = \frac{{40 \times R}}{{100}} \cr & R = \frac{{10}}{4} = 2.5\% {\text{ p}}{\text{.a}}{\text{.}} \cr} $$

$$\eqalign{ & 2P = \frac{{5P \times 8 \times T}}{{10}} \cr & T = 5{\text{ years}} \cr} $$

$$\eqalign{ & \frac{{x \times r \times 3}}{{100}} + \frac{{2x \times \left( {r - 2} \right)}}{{100}} \times 5 = \frac{{x \times r}}{{100}} \times \frac{{34}}{3} \cr & \frac{{2x \times \left( {r - 2} \right) \times 5}}{{100}} = \frac{{x \times r}}{{100}} \times \frac{{34}}{3} - \frac{{x \times r \times 3}}{{100}} \cr & \frac{{2x \times \left( {r - 2} \right) \times 5}}{{100}} = \frac{{\left( {34r - 9r} \right) \times x}}{{300}} \cr & 6\left( {r - 2} \right) \times 5 = 25r \cr & \frac{{36x}}{{100}} + \frac{{2x \times 10}}{{100}} \times 5 = 13600 \cr & \frac{{136x}}{{100}} = 13600 \cr & x = {\text{Rs}}{\text{. }}10000 \cr} $$

$$\eqalign{ & {\bf{Given:}} \cr & {P_1} = 7000,\,{T_1} = 3{\text{ years, }}{R_1} = 5\% \cr & {P_1} = 7000,\,{T_2} = 3{\text{ years, }}{R_2} = 6\frac{1}{3}\% \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{{\text{Principal amout}} \times {\text{Rate of interest}} \times {\text{Time}}}}{{100}} \cr & {\bf{Calculation:}} \cr & {\text{S}}{\text{.I}}{{\text{.}}_1} = \frac{{{P_1} \times {R_1} \times {T_1}}}{{100}} \cr & = \frac{{7000 \times 5 \times 3}}{{100}} \cr & = 1050 \cr & {\text{S}}{\text{.I}}{{\text{.}}_1}{\text{ for one year}} = \frac{{1050}}{3} = 350 \cr & {\text{S}}{\text{.I}}{{\text{.}}_2} = \frac{{{P_1} \times {R_2} \times {T_2}}}{{100}} \cr & = \frac{{7000 \times \frac{{19}}{3} \times 3}}{{100}} \cr & = 1330 \cr & {\text{S}}{\text{.I}}{{\text{.}}_2}{\text{ for one year}} = \frac{{1330}}{3} = 443.33 \cr & {\text{Gain for one year}} = 443.33 - 350 = 93.33 \cr & \therefore {\text{He gain in the transaction per year 93}}{\text{.33}} \cr} $$

$$\eqalign{ & {\text{Annual instalment}} = \frac{{{\text{due debt}} \times 100}}{{100 \times t + rt\left( {\frac{{t - 1}}{2}} \right)}} \cr & = \frac{{5664 \times 100}}{{100 \times 4 + 4 \times 12 \times \frac{3}{2}}} \cr & = \frac{{5664 \times 100}}{{472}} \cr & = {\text{Rs}}{\text{. }}1200 \cr} $$

Formula used:
A = $${\text{P}}\frac{{\left( {1 + {\text{RT}}} \right)}}{{100}}$$
A → Amount
P → Principal
R → Rate
T → Time
Calculation:
A sum at simple interest becomes two times in 8 years
⇒ 2P = $$\frac{{{\text{P}}\left( {1 + {\text{R}} \times {\text{8}}} \right)}}{{100}}$$
⇒ R = $$\frac{{100}}{8}$$
⇒ R = 12.5
∴ The rate of interest is 12.5%
The time in which the same sum will be 4 times
⇒ 4P = $$\frac{{{\text{P}}\left( {1 + 12.5 \times {\text{T}}} \right)}}{{100}}$$
⇒ 300 = 12.5T
⇒ T = 24
∴ The sum will be 4 times in 24 years

$$\eqalign{ & R = 9\% \cr & P = 3270 \cr & t = 3 \cr & {\text{EMI}} = \frac{{P \times 100}}{{100t + \left[ {\left( {t - 1} \right) + \left( {t - 2} \right)\,...} \right] \times R}} \cr & = \frac{{3270 \times 100}}{{100 \times 3 + \left[ {2 + 1} \right] \times 9}} \cr & = \frac{{3270 \times 100}}{{327}} \cr & = 1000 \cr} $$

$$\eqalign{ & 6\frac{1}{2}\% \to 1071.20 \cr & 1\% \to 164.80 \cr & 100\% \to 16480 \cr & {\text{SI}} = \frac{{16480 \times 5 \times 10}}{{100}} = 8240 \cr} $$

\[\begin{array}{*{20}{c}} A&B \\ x&{36000 - x} \end{array}\]
$$\eqalign{ & {\text{As per question}} \cr & x \times 30 = \left( {36000 - x} \right) \times 60 \cr & x = 72000 - 2x \cr & x = 24000 \cr & {\text{So interest from }}A \cr & = 24000 \times \frac{{30}}{{100}} \cr & = 7200 \cr} $$

$$\eqalign{ & \left( {\frac{{P \times 5 \times 3}}{{100}}} \right) = 3\left( {\frac{{Q \times 7 \times 4}}{{100}}} \right) \cr & P = Q \times \frac{{28}}{5} \cr & P = 5.6Q \cr} $$