Question : If the annual rate of simple interest increases from $11\%$ to $17 \frac{1}{2} \%$, then a person's yearly income increases by INR 1,071.20. The simple interest (in INR) on the same sum at 10% for 5 years is:
Option 1: 16,480
Option 2: 9,120
Option 3: 8,240
Option 4: 7,250
Correct Answer: 8,240
Solution : Difference between two rates $= 17\frac{1}{2}\% – 11\% = \frac{13}{2}\% = 6.5\%$ We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ ⇒ $1071.20=\frac{\text{Principal}×6.5×1}{100}$ $\therefore$ Principal = $\frac{107120}{6.5} = 16480$ Now, simple interest for 5 years at the rate of 10% per annum ⇒ Simple Interest $=\frac{16480 × 10 × 5}{100} = 8240$ Hence, the correct answer is INR 8,240.
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