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
Let total capital = ₹x
- 1/3 at 7% → interest = (1/3 × x × 7%)
- 1/4 at 8% → interest = (1/4 × x × 8%)
- Remaining = 1 − (1/3 + 1/4) = 5/12 at 10%
Total interest:
= x[(1/3 × 7%) + (1/4 × 8%) + (5/12 × 10%)]
= x[(7/300) + (8/400) + (50/1200)]
= x[(28 + 24 + 50)/1200]
= x(102/1200)
= x(17/200)
Given interest = ₹1496:
x × 17/200 = 1496
x = 1496 × 200 / 17
x = ₹17,600