Q63
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 = ?
A.
Rs. 60000
B.
Rs. 72000
AnswerC.
Rs. 62000
D.
Rs. 54000
Answer: Option B
Solution
Answer: Option B
Solution:
Rate % = 10%,Time = 1 year
Case (I) : When interest is calculated yearly, Rate = 10%
Case (II) : When interest is calculated half yearly
\begin{aligned} & \Rightarrow {\text{New rate }}\% = \frac{{10}}{2} = 5\% \\ & {\text{Time = 1}} \times {\text{2}} = {\text{2 years}} \\ & {\text{Effective rate}}\% \\ & {\text{ = 5 + 5 + }}\frac{{5 \times 5}}{{100}} = 10.25\% \\ & {\text{Difference in rates}} \\ & {\text{ = }}\left( {10.25 - 10} \right)\% = 0.25\% \\ & {\text{According to the question,}} \\ & {\text{0}}{\text{.25% of sum = Rs 180}} \\ & {\text{Sum = }}\frac{{180}}{{0.25}} \times 100 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs. }}72000 \\\end{aligned}