Multiple choice

A bag contains $50 p, 25 p$ and $10 p$ coins in the ratio $5 :9 : 4$ which amounts to Rs. $206$. Find the number of coins of each type in the given order.

  1. $200, 360, 160$
  2. $100, 80, 120$
  3. $40, 80, 160$
  4. $222, 322, 440$
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A Correct answer
Explanation

Let coins be 5x, 9x, 4x. Values: 5x*0.5 + 9x*0.25 + 4x*0.10 = 206. 2.5x + 2.25x + 0.4x = 206. 5.15x = 206. x = 40. Coins: 5*40=200, 9*40=360, 4*40=160.

AI explanation

Since the coin values are 50 paise, 25 paise and 10 paise, their monetary contribution ratio is calculated by multiplying the coin ratio by their values, giving (5 times 0.50) : (9 times 0.25) : (4 times 0.10), which simplifies to a ratio of 25 : 22.5 : 4 or 50 : 45 : 8. Multiplying this ratio by 4 gives the exact amounts of Rs. 200, Rs. 180 and Rs. 32, which sum to Rs. 412, meaning the multiplier to reach the total Rs. 206 is exactly half. Dividing the original coin ratio parts by two for each denomination (5x, 9x and 4x) shows x equals 40, resulting in 200 coins of 50 paise, 360 coins of 25 paise and 160 coins of 10 paise.

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