Question
On a certain sum of money, the difference between the compound interest for a year payable half yearly, and the simple interest for a year is Rs. 180. If the rate of interest in both the cases is 10%, then the sum is = ?
Answer: Option B
Rate % = 10%,
Time = 1 year
Case (I) : When interest is calculated yearly, Rate = 10%
Case (II) : When interest is calculated half yearly
$$\eqalign{
& \Rightarrow {\text{New rate }}\% = \frac{{10}}{2} = 5\% \cr
& {\text{Time = 1}} \times {\text{2}} = {\text{2 years}} \cr
& {\text{Effective rate}}\% \cr
& {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \cr
& {\text{Difference in rates}} \cr
& {\text{ = }}\left( {10.25 - 10} \right)\% = 0.25\% \cr
& {\text{According to the question,}} \cr
& {\text{0}}{\text{.25% of sum = Rs 180}} \cr
& {\text{Sum = }}\frac{{180}}{{0.25}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}72000 \cr} $$
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Rate % = 10%,
Time = 1 year
Case (I) : When interest is calculated yearly, Rate = 10%
Case (II) : When interest is calculated half yearly
$$\eqalign{
& \Rightarrow {\text{New rate }}\% = \frac{{10}}{2} = 5\% \cr
& {\text{Time = 1}} \times {\text{2}} = {\text{2 years}} \cr
& {\text{Effective rate}}\% \cr
& {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \cr
& {\text{Difference in rates}} \cr
& {\text{ = }}\left( {10.25 - 10} \right)\% = 0.25\% \cr
& {\text{According to the question,}} \cr
& {\text{0}}{\text{.25% of sum = Rs 180}} \cr
& {\text{Sum = }}\frac{{180}}{{0.25}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}72000 \cr} $$
Was this answer helpful ?
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