A bag contains ₹ 1, 50 paisa and 25 paisa coins in the ratio 25 : 9 : 5. If total amount in the bag is 2460 ₹ , then the number of 50 paisa coins in the bag is -

Correct — option (2), 720.

The ratio 25 : 9 : 5 counts coins, and the coins have different values. So turn the count ratio into money first.

Step 1 — value of one set of 25, 9 and 5 coins.
₹ 1 coins: 25 × ₹ 1 = ₹ 25
50 paise coins: 9 × ₹ 0.50 = ₹ 4.50
25 paise coins: 5 × ₹ 0.25 = ₹ 1.25
One set = 25 + 4.50 + 1.25 = ₹ 30.75

Step 2 — number of sets in the bag.
2460 ÷ 30.75 = 80

Step 3 — number of 50 paise coins.
9 × 80 = 720

Check:
₹ 1 coins: 25 × 80 = 2,000 coins, worth ₹ 2,000
50 paise coins: 720 coins, worth ₹ 360
25 paise coins: 5 × 80 = 400 coins, worth ₹ 100
Total = 2,000 + 360 + 100 = ₹ 2,460

The idea to remember: when a ratio counts coins, weight each term by its face value before sharing out the total amount.

Why the others are wrong

• (1)
  1760 — 1760 fifty-paise coins would need far more money than the bag holds. In the ratio 9 : 25, they would go with 1760 × 25 ÷ 9 ≈ 4,889 ₹ 1 coins, worth about ₹ 4,889 on their own.

  The whole bag is worth ₹ 2,460. The value set of ₹ 30.75 gives 80 sets and 9 × 80 = 720.

• (3)
  580 — 580 is not a multiple of 9 (580 ÷ 9 ≈ 64.4). With counts in the ratio 25 : 9 : 5, the 50 paise coins number 9 × (number of sets), a multiple of 9.

  The bag holds 80 sets, so the count is 9 × 80 = 720.

• (4)
  360 — 360 is the value in rupees of the 50 paise coins, not their number. Each is worth half a rupee, so 720 coins make ₹ 360.

  As a count, 360 = 9 × 40 would mean only 40 sets, worth 40 × ₹ 30.75 = ₹ 1,230, half of the ₹ 2,460 in the bag.

A ratio compares quantities of the same kind. Here 25 : 9 : 5 compares numbers of coins, not their worth.

To work with money, multiply each term by its value: 25 × ₹ 1 : 9 × ₹ 0.50 : 5 × ₹ 0.25 = 25 : 4.5 : 1.25, which is 100 : 18 : 5.

The value ratio gives the same answer. 100 + 18 + 5 = 123 parts; ₹ 2,460 ÷ 123 = ₹ 20 per part; the 50 paise coins are worth 18 × 20 = ₹ 360, which is 720 coins.

When counts are in a ratio whose terms, taken all together, have no common factor other than 1 (25, 9 and 5 have none), each count is its ratio term times a whole number.

Key facts

• 100 paise = ₹ 1, so a 50 paise coin is ₹ 0.50 and a 25 paise coin is ₹ 0.25.
• Coins in the ratio 25 : 9 : 5 by number are in the ratio 25 : 4.5 : 1.25, or 100 : 18 : 5, by value.
• One set of 25, 9 and 5 such coins is worth ₹ 30.75, and ₹ 2,460 holds 80 sets.
• The bag holds 2,000 ₹ 1 coins, 720 fifty-paise coins and 400 twenty-five-paise coins.
• The 720 fifty-paise coins are worth ₹ 360.

Common traps

• Sharing the amount in the count ratio. ₹ 2,460 × 9 ÷ 39 ≈ ₹ 567.69 treats 25 : 9 : 5 as a ratio of money, which it is not.
• Stopping at the value. The 50 paise coins are worth ₹ 360; the stem asks for their number, 720.
• Mixing paise and rupees. 9 × 50 = 450 is in paise, which is ₹ 4.50, not ₹ 450.

UnlockIAS will link similar questions from RAS Pre 2018 here once that paper is published on this site.

• practice — not a real PYQ

  A purse has ₹ 5, ₹ 2 and ₹ 1 coins in the ratio 2 : 3 : 5 by number. If the total amount is ₹ 420, how many ₹ 2 coins are there?

  • (a)60
  • (b)120
  • (c)126
  • (d)40
  Answer(1) — One set of 2, 3 and 5 coins is worth 10 + 6 + 5 = ₹ 21, so ₹ 420 holds 20 sets and there are 3 × 20 = 60 ₹ 2 coins.

  Option (2) is the value of those coins in rupees; option (3) shares ₹ 420 in the count ratio, 420 × 3 ÷ 10; option (4) is the number of ₹ 5 coins.

• practice — not a real PYQ

  A bag has 50 paise and 25 paise coins in the ratio 3 : 4 by number, worth ₹ 50 in all. How many coins are there in the bag?

  • (a)140
  • (b)200
  • (c)100
  • (d)70
  Answer(1) — One set of 3 and 4 coins is worth 1.50 + 1.00 = ₹ 2.50, so ₹ 50 holds 20 sets of 7 coins: 140 coins.

  Option (2) treats every coin as 25 paise; option (3) treats every coin as 50 paise; option (4) divides ₹ 50 by ₹ 5 instead of ₹ 2.50, giving only 10 sets.