Sarah invested amounts in three different schemes M, N, and O at simple interest rates of 10% p.a., 12% p.a., and 15% p.a. respectively. If the total interest accrued in one year was ₹2282 and the amount invested in Scheme O was 180% of the amount invested in Scheme M and 250% of the amount invested in Scheme N, what was the amount invested in Scheme N?

Correct — C.
O is 180% of M: M = O ÷ 1.8 = 5⁄9 of O
O is 250% of N: N = O ÷ 2.5 = 2⁄5 of O
Let O = 45k (divisible by 9 and 5): M = 25k, N = 18k

One year's interest: 10% of 25k + 12% of 18k + 15% of 45k
= 2.5k + 2.16k + 6.75k = 11.41k
11.41k = 2282, so k = 200

N = 18 × 200 = ₹3600 → option (c)
Check: M = ₹5000, O = ₹9000, interest 500 + 432 + 1350 = ₹2282

Why the others are wrong

• (a)
  ₹3000 — ₹3000 in N puts ₹7500 in O and about ₹4167 in M. One year's interest is then about 417 + 360 + 1125 = ₹1902, not ₹2282.
• (b)
  ₹3200 — ₹3200 in N means O = ₹8000 and M ≈ ₹4444. Interest ≈ 444 + 384 + 1200 = ₹2028, short of ₹2282.
• (d)
  ₹4000 — ₹4000 in N means O = ₹10,000 and M ≈ ₹5556. Interest ≈ 556 + 480 + 1500 = ₹2536, more than ₹2282.

When amounts are tied by percentages, write all of them through one variable, here the amount in O. "O is 180% of M" means O = 1.8 × M, so M is the smaller amount.

Simple interest for one year is just principal × rate, so the total interest is a weighted sum. Taking O as a multiple of 45 keeps every amount whole and leaves one division.

Key facts

• "O is 180% of M" means O = 1.8M, so M = 5⁄9 of O.
• "O is 250% of N" means O = 2.5N, so N = 2⁄5 of O.
• M : N : O = 25 : 18 : 45, which here is ₹5000, ₹3600 and ₹9000.
• One year's simple interest = principal × rate: 10% of 5000 + 12% of 3600 + 15% of 9000 = ₹2282.

Common traps

• Writing M = 1.8 × O: the stem makes O the larger amount, 180% of M
• Reading 250% of N as 250% more than N, which would make O = 3.5N

No directly related past PYQ was found.