Two equal sums of money were lent at simple interest at 11\% p.a. for $3 \frac{1}{2}$ years and $4 \frac{1}{2}$ years respectively. If the difference in interests for two periods was ₹ 412.50, then each sum is:
(a)₹ 3250
(b)₹ 3500
(c)₹ 3750
(d)₹ 4250
Answer
Answer (as printed): C
Explanation
Let each sum be ₹ $x$. Then, $\left(\frac{x \times 11 \times 9}{100 \times 2}\right)-\left(\frac{x \times 11 \times 7}{100 \times 2}\right)=412.50$ $$\Leftrightarrow \quad(99 x-77 x)=82500 \Leftrightarrow 22 x=82500 \Leftrightarrow x=3750 .$$
Explanation as extracted from the printed page; notation may be imperfect.