Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & P = Rs.\,3300 \cr & A = Rs.\,3399 \cr & R = 6\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Let}}\,{\text{the}}\,{\text{time}}\,{\text{be}}\,{\text{n}}\,{\text{years}}{\text{.}} \cr & {\text{Compound}}\,{\text{interest}}\,{\text{is}}\,{\text{taken}}\,{\text{half - yearly}}. \cr & A = P \times {\left[ {1 + \left( {\frac{R}{2} \times 100} \right)} \right]^{2n}} \cr & 3399 = 3300{\left( {1 + \frac{3}{{100}}} \right)^{2n}} \cr & {\left( {1.03} \right)^{2n}} = \frac{{3399}}{{3300}} \cr & {\left( {1.03} \right)^{2n}} = {\left( {1.03} \right)^1} \cr & Thus,\,2n = 1\,year \cr & n = \frac{1}{2}{\text{year}} = 6\,{\text{months}} \cr} $$

$$\eqalign{ & {\text{Value}}\,{\text{of}}\,{\text{maruti}}\,{\text{Van}},\, \cr & {V_0} = Rs.\,196000 \cr & {\text{Rate}}\,{\text{of}}\,{\text{depreciation}},\, \cr & r = 14 {\frac{2}{7}} \% = \frac{{100}}{7}\% ; \cr & {\text{Time}},\,t = 2\,{\text{years}} \cr & {\text{Let}}\,{V_1}\,{\text{is}}\,{\text{the}}\,{\text{value}}\,{\text{after}}\,{\text{depreciation}}. \cr & {V_1} = {V_0} \times {\left[ {1 - \left( {\frac{r}{{100}}} \right)} \right]^t} \cr & {V_1} = 196000 \times {\left[ {1 - \left( {\frac{{\left( {\frac{{100}}{7}} \right)}}{{100}}} \right)} \right]^2} \cr & {V_1} = 196000 \times {\left( {1 - {\frac{1}{7}}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{7-1}{7}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{6}{7}} \right)^2} \cr & {V_1} = \frac{{\left( {196000 \times 36} \right)}}{{49}} \cr & {V_1} = Rs.\,144000 \cr} $$

$$\eqalign{ & {\text{Interest}}\,{\text{for}}\,{\text{the}}\,{\text{last}}\,{\text{5}}\,{\text{years}} \cr & = \frac{{PTR}}{{100}} \cr & = \frac{{360 \times 5 \times 6}}{{100}} = Rs.\,108 \cr & {\text{Interest}}\,{\text{for}}\,{\text{year}} = 540 - 360 = 180 \cr & {\text{So,}}\,{\text{interest}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr & = 180 - 108 = Rs.\,72; \cr & {\text{Now,}}\,{\text{rate}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr & = \frac{{ {72 \times 100} }}{{360 \times 4}} \cr & = 5\% \cr} $$

$$\eqalign{ & {\text{Here,}}\,{\text{time}}\,{\text{interval}}\,{\text{is}}\,{\text{given}}\,{\text{as}}\, \cr & {\text{February}}\,5,\,1994\,{\text{to}}\,{\text{April}}\,18,\,1994 \cr & = 73\,{\text{days}} = \frac{{73}}{{365}} = 0.2\,{\text{years}}. \cr & {\text{Now}}\,{\text{interest}} = \frac{{PTR}}{{100}} \cr & = \frac{{ {700 \times 9 \times 0.2} }}{{100}} \cr & = Rs.\,12.60 \cr} $$

Let Asif lent Rs. X at 14% per year.
Hence, Money lent at 12% = (1500 - x);
Given, total interest = Rs. 186
$$ {\frac{{\left( {x \times 14 \times 1} \right)}}{{100}}} \, + $$    $$ {\frac{{\left[ {\left( {1500 - x} \right) \times 12 \times 1} \right]}}{{100}}} $$      = 186
$$\eqalign{ & \frac{{14x}}{{100}} + \frac{{ {18000 - 12x} }}{{100}} = 186 \cr & 14x + 18000 - 12x = 186 \times 100 \cr & 2x = 18600 - 18000 \cr & x = \frac{{600}}{2} = {\text{Rs}}{\text{. }}300 \cr & {\text{Hence, money lent}}{\kern 1pt} {\text{at }}12\% \cr & = 1500 - 300 \cr & = {\text{Rs}}{\text{.}}\,1200 \cr} $$

Let the rate be R at which Principal P is invested for 2 years.
According to question,
{Interest at Rate (R + 2)}% - (interest at rate R%) = Rs. 60
$$\frac{{\left( {P \times 2 \times \left( {R + 2} \right)} \right)}}{{100}} - $$     $$\frac{{\left( {P \times 2 \times R} \right)}}{{100}}$$   $$ = 60$$
$$\eqalign{ & \frac{{ {2PR + 4P - 2PR} }}{{100}} = 60 \cr & 4P = 60 \times 100 \cr & {\text{Or}},P = \frac{{60 \times 100}}{4} \cr & {\text{Hence}},P = {\text{Rs}}{\text{.}}\,1500 \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{sum}}\,{\text{is}}\,P. \cr & {\text{The}}\,{\text{difference}}\,{\text{between}}\,{\text{compound}}\,{\text{interest}}\,{\text{and}} \cr & \,{\text{simple}}\,{\text{interest}}\,{\text{over}}\,{\text{three}}\,{\text{years}}\,{\text{is}}\,{\text{given}}\,{\text{by}} \cr & = P\left( {\frac{r}{{100}}} \right)2 \times \left\{ {\left( {\frac{r}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \left( {\frac{{20}}{{100}}} \right)2 \times \left\{ {\left( {\frac{{20}}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \frac{4}{{100}} \times \frac{{16}}{5} \cr & 48 = P \times \frac{{64}}{{500}} \cr & {\text{Or}},\,64P = 48 \times 500 \cr & {\text{Hence}},\,P = Rs.\,375 \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{time}}\,{\text{is}}\,T\,{\text{years}}. \cr & {\text{According}}\,{\text{to}}\,{\text{questions}}, \cr & \frac{{1750 \times 9 \times T}}{{100}} = \frac{{\left( {2500 \times 10.5 \times 4} \right)}}{{100}} \cr & Or,\,T = \frac{{ {2500 \times 10.5 \times 4} }}{{1750 \times 9}} \cr & Or,\,T = 6.66 = 6\,{\text{years}}\,{\text{and}}\,8\,{\text{months}} \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{rate}}\,{\text{is}}\,R\% \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & \left[ {\frac{{400 \times 2 \times R}}{{100}}} \right] + \left[ {\frac{{100 \times 4 \times R}}{{100}}} \right] = 60 \cr & 8R + 4R = 60 \cr & {\text{Hence}},\,R = 5\% \cr} $$

$$\eqalign{ & {1^{{\text{st}}}}\,{\text{Method}}: \cr & {\text{Let rate is }}R\% \cr & {\text{Now}}, \cr & P = 100, \cr & A = 400, \cr & I = 400 - 100 = 300, \cr & {\text{Time}},\,T = 10\,{\text{years}} \cr & I = \frac{{PTR}}{{100}} \cr & {\text{Or}},R = \frac{{ {100 \times I} }}{{PT}} \cr & {\text{Or}},R = \frac{{ {100 \times 300} }}{{ {100 \times 10} }} \cr & {\text{Hence}},{\kern 1pt} R = 30\% \cr} $$

2^nd Method :
Here, the sum become 4 times that means 100, become 400.
Rate of such question is given by
$$R = \frac{{{\text{interest}}}}{{{\text{time}}}} = \frac{{300}}{{10}} = 30\% $$

3^rd Method :
Here, 300% of rise in the sum so
$$\eqalign{ & 100 - - - 300\% \uparrow - - - {\kern 1pt} 400; \cr & R = {\frac{{{\text{total}}\,{\text{percentage rise}}}}{{{\text{given time}}}}} \cr & \,\,\,\,\,\,\,\, = \frac{{300\% }}{{10}} \cr & \,\,\,\,\,\,\,\, = 30\% \cr} $$