A person invested a total sum of ₹1900 in three different schemes of simple interest at 2%, 4%, and 5% per annum. At the end of one year, he got the same interest from all three schemes. What was the amount (in ₹) invested at 4%?

Correct — B.
Let each scheme's one-year interest be k.

At 2%: 0.02 × a = k, so a = 50k
At 4%: 0.04 × b = k, so b = 25k
At 5%: 0.05 × c = k, so c = 20k

Add: 50k + 25k + 20k = 95k = 1900, so k = 20
Amount at 4%: b = 25 × 20 = ₹500 → option (b)

Check: ₹1000, ₹500 and ₹400 each earn ₹20 in a year.

Why the others are wrong

• (a)
  ₹1000 — ₹1000 is the amount at 2%, not at 4%. Doubling the rate halves the sum needed for the same ₹20, so the 4% scheme holds ₹500.
• (c)
  ₹400 — ₹400 is the amount at 5%: 5% of 400 = ₹20. The question asks for the 4% scheme.
• (d)
  ₹350 — ₹350 at 4% earns ₹14. Matching ₹14 at 2% and 5% needs ₹700 and ₹280, a total of ₹1330, not ₹1900.

When different sums earn the same interest over the same time, each sum is inversely proportional to its rate: the lower the rate, the more money it needs.

So a : b : c = 1⁄2 : 1⁄4 : 1⁄5. Multiply by 20 to clear the fractions: 10 : 5 : 4.

The parts total 19, and 1900 ÷ 19 = 100, so the sums are ₹1000, ₹500 and ₹400.

Key facts

• Equal simple interest over equal time means principal × rate is the same for every part
• Rates of 2%, 4% and 5% give principals in the ratio 10 : 5 : 4
• Each part here earns ₹20 in the year

Common traps

• Splitting ₹1900 in the ratio of the rates, 2 : 4 : 5, instead of their reciprocals
• Finding all three sums and then answering with the one at 2% or 5%

No directly related past PYQ was found.