Question : If the annual rate of simple interest increases from $11\%$ to $17 \frac{1}{2} \%$, a person's yearly income increases by Rs. 1,071.20. The principal amount invested (in Rs.) is:
Option 1: 19,120
Option 2: 16,480
Option 3: 17,250
Option 4: 10,710
Correct Answer: 16,480
Solution :
The increase in yearly income is due to the increase in interest rates.
Given that the increase in income is Rs. 1,071.20 and the increase in interest rate is $17\frac{1}{2}\% - 11\% = 6\frac{1}{2}\% = \frac{13}{2}\%$
Principal = $\frac{\text{Increase in income}}{\text{Increase in interest rate}}×100 = \frac{1071.20}{ \frac{13}{2}}×100$ = Rs. 16,480
Hence, the correct answer is 16,480.
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