An individual invested certain amounts in three different schemes P, Q, and R at simple interest rates of 7% p.a., 9% p.a., and 11% p.a. respectively. If the total interest accrued in one year was ₹2520 and the amount invested in Scheme R was 250% of the amount invested in Scheme P and 300% of the amount invested in Scheme Q, what was the amount invested in Scheme P?

Correct — C. Turn the percentages into one ratio.

R = 250% of P, so P = R ÷ 2.5 = 2R⁄5
R = 300% of Q, so Q = R ÷ 3 = R⁄3
Take R = 15k: P = 6k, Q = 5k, R = 15k

One year's interest, in rupees:
7% of 6k + 9% of 5k + 11% of 15k
= (42k + 45k + 165k) ÷ 100 = 2.52k

2.52k = 2520, so k = 1000
P = 6k = ₹6000 → option (c)

Why the others are wrong

• (a)
  ₹5000 — ₹5000 is the amount in Scheme Q, since Q = 5k = ₹5000. With P = ₹5000 the year's interest would be 0.42 × 5000 = ₹2100, not ₹2520.
• (b)
  ₹5500 — ₹5500 gives a year's interest of 0.42 × 5500 = ₹2310, short of ₹2520. Every rupee in P carries 42 paise of total interest, so P = 2520 ÷ 0.42.
• (d)
  ₹6500 — ₹6500 overshoots: 0.42 × 6500 = ₹2730 of interest, ₹210 more than the ₹2520 given.

When every amount is tied to one scheme by a percentage, reduce them to a single ratio before touching the rates.

R = 250% of P and R = 300% of Q give P : Q : R = 6 : 5 : 15. The year's interest is then a weighted sum of the rates: (6 × 7 + 5 × 9 + 15 × 11)% of k = 2.52k, which is 42% of P.

Key facts

• R = 250% of P means P = 2⁄5 of R.
• R = 300% of Q means Q = 1⁄3 of R.
• P : Q : R = 6 : 5 : 15, and the total interest is 0.42 × P.

Common traps

• Reading "R was 300% of Q" as Q = 3R, which makes Q the largest amount.
• Answering the amount in Scheme Q, ₹5000, instead of Scheme P.

No directly related past PYQ was found.