| A money-lender borrows money at 5% per annum and pays interest at the end of the year. He lends it at 8% per annum compound interest compounded half-yearly and receives the interest at the end of the year. Thus, he gains Rs. 118.50 in a year. The amount of money he borrows is |
A) Rs. 3450
B) Rs. 3600
C) Rs. 3750
D) Rs. 3900
Correct Answer: C
Solution :
| Let the money borrowed be Rs. x. |
| Interest paid by the money lenders \[=\text{Rs}\text{. }\left( \frac{x\times 1\times 5}{100} \right)=\frac{x}{20}\] |
| Interest received by the money lender |
| \[=\left[ x\times {{\left( 1+\frac{8/2}{100} \right)}^{2\times 1}}-x \right]\] |
| \[=\left[ x\times {{\left( 1+\frac{4}{100} \right)}^{2}}-x \right]\] |
| \[=\left[ x\times \frac{26}{25}\times \frac{26}{25}-x \right]=\text{Rs}\text{. }\left[ x\times \left( \frac{676}{625}-1 \right) \right]\] |
| \[=\text{Rs}\text{. }\left[ x\times \left( \frac{51}{625} \right) \right]\vec{=}\text{Rs}\text{. }\frac{51x}{625}\] |
| Now, \[\left( \frac{51x}{625}-\frac{x}{20} \right)=118.50\] |
| \[\Rightarrow \] \[\frac{204x-125x}{625\times 4}=118.50\] |
| \[\Rightarrow \] \[\frac{79x}{625\times 4}=118.50\] |
| \[\Rightarrow \] \[x=\left( \frac{118.50\times 625\times 4}{79} \right)=3750\] |
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