Divyansh invested 1/4 of his capital at 10%, 1/5 at 20% and the remaining at 30% simple interest per annum, respectively. If his annual income is ₹3,220, then find the capital (in₹).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 14,000.
Let the total capital be ₹x.
Investments: 1/4 of x at 10% → (1/4)x at 10%
1/5 of x at 20% → (1/5)x at 20%
Remaining = 1 - (1/4 + 1/5) = 1 - (9/20) = 11/20 of x at 30%
Income from each: From 1/4 x at 10%: = (1/4)x × 10% = (1/4)x × (10/100) = x/40
From 1/5 x at 20% = (1/5)x × 20% = (1/5)x × (20/100) = x/25
From 11/20 x at 30% = (11/20)x × 30% = (11/20)x × (30/100) = (33x)/200
Total income = x/40 + x/25 + 33x/200 = 3220
⇒ (200)(x/40) + (200)(x/25) + (200)(33x/200) = 3220 × 200
→ 5x + 8x + 33x = 644000
→ 46x = 644000
→ x = 644000 / 46
→ x = ₹14,000