Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. }}16800 \cr & {\text{R}} = 6\frac{1}{4}\% = \frac{{25}}{4}\% \cr & {\text{T}} = 9\,{\text{mths}} = \frac{3}{4}{\text{yr}}{\text{.}} \cr & \therefore {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {16800 \times \frac{{25}}{4} \times \frac{3}{4} \times \frac{1}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,787.50 \cr} $$

$$\eqalign{ & {\text{Let the principal}} \cr & {\text{ = 9 units }} \cr & {\text{Hence simple interest}} \cr & {\text{ = }}\frac{4}{9} \times {\text{9 = 4 units}} \cr & {\text{Let,}} \cr & {\text{Rate of interest = R% }} \cr & {\text{R = T (given)}} \cr & {\text{By using formula}} \cr & \boxed{{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & 4 = \frac{{9 \times {\text{R}} \times {\text{R}}}}{{100}} \cr & {{\text{R}}^2} = \frac{{400}}{9} \cr & {\text{R = }}\frac{{20}}{3} = 6\frac{2}{3}\% \cr} $$

$$\eqalign{ & {\text{Let principal = 5 units}} \cr & {\text{Hence interest}} \cr & {\text{ = 5}} \times \frac{2}{5} \cr & {\text{ = 2 units}} \cr & {\text{Time = 10 years}} \cr & {\text{By using formula, }} \cr & {\text{Rate% = }}\frac{2}{5} \times \frac{{100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 4% }} \cr} $$

$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1750}} \cr & {\text{Let the first part = }}x \cr & {\text{Hence second part}} \cr & {\text{ = }}\left( {1750 - x} \right) \cr & {\text{According to the question,}} \cr & \Rightarrow x \times \frac{8}{{100}} \times 1 = \left( {1750 - x} \right) \times \frac{6}{{100}} \times 1 \cr & \Rightarrow 4x = 5250 - 3x \cr & \Rightarrow 7x = 5250 \cr & \Rightarrow x = 750 \cr & {\text{First part = Rs}}{\text{. 750}} \cr & \therefore {\text{ Second part}} \cr & {\text{ = Rs}}{\text{. }}\left( {1750 - 750} \right) \cr & {\text{ = Rs}}{\text{. 1000}} \cr & {\text{Required interest}} \cr & {\text{ = 750}} \times \frac{8}{{100}} \cr & {\text{ = Rs}}{\text{. 60}} \cr} $$

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let, Principal = 100 units in both cases

		1st part		2nd part		Total
Principal	→	100×3	:	100×4	+→	700 units
Interest	→	8×3	:	6×4

Note : Interest is same in both cases
According to the question,
$$\eqalign{ & {\text{700 units = Rs}}{\text{. 1750}} \cr & {\text{1 unit = Rs}}{\text{. }}\frac{{1750}}{{700}} \cr & {\text{24 units = Rs}}{\text{. }}\frac{{1750}}{{700}} \times 24 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 60}} \cr & {\text{Hence, required interest}} \cr & {\text{ = Rs}}{\text{. 60}} \cr} $$

$$\eqalign{ & {\text{Gain in 2 years}} \cr & = {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \cr & = {\text{Rs}}{\text{.}}\left( {625 - 400} \right) \cr & = {\text{Rs}}{\text{. }}225 \cr & \therefore {\text{Gain 1 year}} = {\text{Rs}}{\text{.}}\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{. }}112.50 \cr} $$

Let the amounts invested in schemes A and B be Rs. 5x and 4x respectively.
then,
5x = 20000
⇒ x = 4000
∴ Amount invested in scheme B = Rs. 16000
Total interest received on maturity
$$ = {\text{Rs}}{\text{.}}\left[ {{\text{120}}\% {\text{ of}}\left( {\frac{{{\text{20000}} \times {\text{8}} \times {\text{5}}}}{{{\text{100}}}}} \right) + \left( {\frac{{{\text{16000}} \times {\text{9}} \times {\text{5}}}}{{{\text{100}}}}} \right)} \right]$$
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left( {{\text{120}}\% \,{\text{of}}\,{\text{8000}} + {\text{7200}}} \right) \cr & = {\text{Rs}}{\text{.}}\,\left( {{\text{9600}} + {\text{7200}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{16800}} \cr & \therefore {\text{Total amount}} \cr & = {\text{Rs}}{\text{.}}\,\left( {{\text{20000}} + {\text{16000}} + {\text{16800}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{52800}} \cr} $$

Let the sum at 8% be Rs. x
Let the sum at 5% be 1550 - x
According to the given condition,
$$\eqalign{ & \frac{{{\text{x}} \times 8 \times 3}}{{100}} + \frac{{\left( {1550 - {\text{x}}} \right) \times 5 \times 3}}{{100}} = 300 \cr & \Rightarrow \frac{{24{\text{x}} + \left( {1550 - {\text{x}}} \right) \times 15}}{{100}} = 300 \cr & \Rightarrow \frac{{24{\text{x}} + 23250 - 15{\text{x}}}}{{100}} = 300 \cr & \Rightarrow 24{\text{x}} - 15{\text{x}} = 30000 - 23250 \cr & \Rightarrow 24{\text{x}} - 15{\text{x}} = 6750 \cr & \Rightarrow 9{\text{x}} = 6750 \cr & \Rightarrow {\text{x}} = \frac{{6750}}{9} = 750 \cr & \frac{{{\text{Money lent at 5}}\% }}{{{\text{Money lent at 8}}\% }} \cr & = \frac{{1550 - 750}}{{750}} \cr & = \frac{{800}}{{750}} \cr & = \frac{{16}}{{15}} \cr & = 16:15 \cr} $$

(Principal + Interest) in 5 years → 520
(Principal + Interest) in 7 years → 568
$$\eqalign{ & \therefore {\text{Interest in 2 years = 48}} \cr & \therefore {\text{I = }}\frac{{{\text{48}}}}{2}{\text{ }} \cr & \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 24 in one year}} \cr & \therefore {\text{P = 520 - 24}} \times {\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 400}} \cr} $$

Let initial capital = 100 units

According to the question,
$$\eqalign{ & \frac{1}{4}{\text{unit = Rs}}{\text{. 61}}{\text{.50}} \cr & {\text{1 unit = Rs}}{\text{. 61}}{\text{.50}} \times {\text{4}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 246}} \cr & {\text{100 units = Rs}}{\text{. 24600}} \cr} $$
Hence,
Required capital = Rs. 24600

Alternate
Difference in percentage
$$\eqalign{ & {\text{ = 8% }} - \frac{{31}}{4}\% \cr & \Leftrightarrow \frac{1}{4}\% = 61.50 \cr & \Leftrightarrow 100\% = 24600 \cr} $$

$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{.}}\,{\text{450}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 81}} \cr & {\text{R}} = {\text{4}}{\text{.5}}\% \cr & {\text{Time}} \cr & = \left( {\frac{{100 \times 81}}{{450 \times 4.5}}} \right){\text{years}} \cr & = 4\,{\text{years}}{\text{}} \cr} $$