A person invested a total sum of ₹2200 in three different schemes of simple interest at 4%, 5%, and 10% per annum. At the end of one year, he got the same interest from all three schemes. What was the amount (in ₹) invested at 5%?

Correct — B. Equal interest means each sum is inversely proportional to its rate.

Let each scheme earn ₹I in one year
Sums: I ÷ 0.04 = 25I, I ÷ 0.05 = 20I, I ÷ 0.10 = 10I

Add them: 25I + 20I + 10I = 55I = 2200
So I = ₹40
Sum at 5%: 20 × 40 = ₹800 → option (b)

Why the others are wrong

• (a)
  ₹1000 — ₹1000 is the sum at 4%, not 5%: 4% of 1000 = ₹40. The lowest rate needs the largest sum to earn the same ₹40.
• (c)
  ₹600 — ₹600 at 5% earns ₹30. Matching ₹30 needs ₹750 at 4% and ₹300 at 10%, and 750 + 600 + 300 = ₹1650, not ₹2200.
• (d)
  ₹400 — ₹400 is the sum at 10%: 10% of 400 = ₹40. The highest rate needs the smallest sum, and the question asks for the 5% scheme.

If P₁ × R₁ = P₂ × R₂ = P₃ × R₃ (same time, same interest), the sums are in the ratio 1⁄R₁ : 1⁄R₂ : 1⁄R₃.

1⁄4 : 1⁄5 : 1⁄10, multiplied by 20, is 5 : 4 : 2, which is 11 parts.

₹2200 ÷ 11 = ₹200 a part, so the sums are ₹1000, ₹800 and ₹400. Each earns ₹40 in a year.

Key facts

• Equal simple interest over equal time means principal × rate is the same for each sum.
• Rates 4%, 5% and 10% give sums in the ratio 5 : 4 : 2.
• Check: 4% of 1000 = 5% of 800 = 10% of 400 = ₹40.

Common traps

• Splitting ₹2200 in the ratio of the rates, 4 : 5 : 10, instead of their reciprocals.
• Solving correctly and then reading off the sum at 4% or 10%.

No directly related past PYQ was found.