A man invested on simple interest, \(\displaystyle\frac{1}{4}\) of his capital at 7% p.a., another \(\displaystyle\frac{1}{4}\) of the capital at 8% p.a. and the remaining capital at 10% p.a. He earned Rs. 700 as interest in one year. Find his total capital invested.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 8000
Simple interest for one year is rate × principal ÷ 100, so the interest of each part is found and the three are added. Let the capital be \(C\); the remaining part is \(\displaystyle\frac{1}{2}C\).
Interest on \(\displaystyle\frac{1}{4}C\) at 7%: \(\displaystyle\frac{7C}{400}\)
Interest on \(\displaystyle\frac{1}{4}C\) at 8%: \(\displaystyle\frac{8C}{400}\)
Interest on \(\displaystyle\frac{1}{2}C\) at 10%: \(\displaystyle\frac{20C}{400}\)
Total: \(\displaystyle\frac{35C}{400}=700\), so \(C=\) Rs. 8000