| If the difference between the compound interest, compounded semi-annually and the simple interest on a sum at 10% per annum for one year is 25, then the sum is |
A) Rs. 9000
B) Rs. 9500
C) Rs. 10000
D) Rs. 10500
Correct Answer: C
Solution :
| Let the sum be Rs. x. |
| Then, \[A=x{{\left( \frac{200+10}{200} \right)}^{2}}=x\times \frac{441}{400}\] |
| \[CI=\frac{441}{400}x-x=\frac{41}{400}x\] |
| \[SI=\frac{x\times 10\times 1}{100}=\frac{x}{10}\] |
| Now, \[CI-SI=\frac{41}{400}x-\frac{x}{10}=\frac{x}{400}\] |
| \[\Rightarrow \] \[25=\frac{x}{400}\] |
| \[\Rightarrow \] \[x=25\times 400=\text{Rs}\text{. 10000}\] |
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