Gopal invested one third of his capital at 7%, one fourth at 8% and the remaining at 10% rate of simple interest. If he earned ₹1,496 as interest in one year, then find his capital (in ₹).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 17,600
For one year, simple interest is rate × principal. Each part of the capital earns its own rate, so the whole capital earns a weighted average rate: each rate multiplied by the fraction of the capital that earns it.
Fraction at 10%: \(\displaystyle1-\frac{1}{3}-\frac{1}{4}=\frac{5}{12}\)
Average rate:
\(\displaystyle\frac{1}{3}\times7+\frac{1}{4}\times8+\frac{5}{12}\times10\)
\(\displaystyle=\frac{14}{6}+\frac{12}{6}+\frac{25}{6}=\frac{51}{6}=8.5\%\)
8.5% of the capital is the year’s interest of ₹1,496, so capital \(\displaystyle=\frac{1496\times100}{8.5}=17600\)
His capital is ₹17,600.