Interest - Aptitude MCQ Questions and Solutions with Explanations

  Let Sum be Rs. x and Let S.I. = Rs. x
$$\eqalign{ & {\text{Time}} = 10\,{\text{years}} \cr & \therefore {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr & = \frac{{x \times 100}}{{x \times 10}} \cr & = 10\% \,{\text{per}}\,{\text{annum}}{\text{.}} \cr} $$

$$\eqalign{ & {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{5400 \times 100}}{{15000 \times 3}} \cr & = 12\% \,{\text{Per annum}}{\text{.}} \cr} $$

Let the amount invested in scheme A be Rs. x and that in B be Rs. 3x.
Then,
$$\eqalign{ & = \frac{{x \times 4 \times 8}}{{100}} + \frac{{3x \times 2 \times 13}}{{100}} = 1320 \cr & or,\,\frac{{32x}}{{100}} + \frac{{78x}}{{100}} = 1320 \cr & or,\,\frac{{110x}}{{110}} = 1320 \cr & \therefore x = \frac{{1320 \times 100}}{{110}} \cr & = {\text{Rs}}{\text{. 1200}}. \cr} $$

S.I for 1 year = 5832 – 5182 = Rs. 650
S.I for 2 years = Rs. 1300
P = 5182 – 1300
= Rs. 3882

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. of 2}}{\text{.5 years}} \cr & {\text{ = 5500}} - {\text{4000}} \cr & {\text{ = 1500}} \cr & {\text{S}}{\text{.I}}{\text{. of 2 years}} \cr & {\text{ = }}\frac{{1500}}{{2.5}} \times {\text{2}} \cr & {\text{ = 1200}} \cr & {\text{So, Principal}} \cr & {\text{ = 4000}} - {\text{SI of 2 years}} \cr & \Rightarrow {\text{Principal = 4000}} - 1200 \cr & \Rightarrow {\text{Principal = 2800}} \cr & {\text{r}}\% {\text{ = }}\frac{{1200}}{{2800 \times 2}} \times {\text{100}} \cr & \,\,\,\,\,\,\,\,{\text{ = 21}}\frac{3}{7}\% \cr} $$

Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$$
and Amount get by Shyam after 6 years
$$ = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$$
But both get equal amount
$$\therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times $$       $${\left( {1 + \frac{4}{{100}}} \right)^6}$$
$$\eqalign{ & \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr & \Rightarrow 15625x = 4573275200 - 17576x \cr & \Rightarrow 33201x = 4573275200 \cr & \Rightarrow x = 137745.022 \cr} $$
So, Ram will get Rs. 137745.022

$$\eqalign{ & \frac{1}{4}:\frac{1}{5}:\frac{1}{8} \cr & 10:8:5 \cr & {\text{Amount invested at }}5\% \cr & = \frac{8}{{23}} \times 57,500 \cr & = 20,000 \cr} $$

$$\eqalign{ & {\text{Cash amount}} = 25000 \cr & {\text{Down payment}} = 2500 \cr & {\text{Remaining amount}} = 22500 \cr & {\text{Rate}} = 24\% \,{\text{p}}{\text{.a}} \cr & {\text{12 month}} \to 24\% \cr & \to \frac{{24}}{{12}} \times 100 = \frac{1}{{50}} \cr & 4{\text{ month}} \to 8\% \cr & \Rightarrow {\text{Total amount}} = 22500 \times \frac{{108}}{{100}} \cr & = 24300 \cr} $$
\[\begin{array}{*{20}{c}} {50}& - &{50} \\ {50}& - &{51} \\ {50}& - &{52} \\ {50}& - &{\mathop {53}\limits_{\_\_\_\_\_\_} } \\ {}&{}&{206} \end{array}\]
$$\eqalign{ & {\text{EMI}} = \frac{{24300 \times 50}}{{206}} \cr & = 5898.05 \cr & = 5900 \cr} $$

$$\eqalign{ & {\text{3 years total rate}} = 14 \times 3 = 42\% \cr & {\text{5 years total rate}} = 14 \times 5 = 70\% \cr & {\text{Gap}} = 28\% \to 4200 \cr & {\text{Sum}} = \frac{{4200}}{{28}} \times 100 = {\text{Rs}}{\text{. }}15,000 \cr} $$

$$\eqalign{ & {\text{S}}{\text{.}}{{\text{I}}_1} = 2 \times {\text{S}}{\text{.}}{{\text{I}}_2} \cr & \frac{{x \times 20 \times 21}}{{100 \times 3 \times 5}} = 2 \times \frac{{y \times 4 \times 11}}{{100 \times 4}} \cr & 28x = 22y \cr & x:y = 22:28 \cr & {\text{Ratio of second part of first part}} \cr & y:x = 28:22 = 14:11 \cr} $$