A bag has ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in total. How many coins of each kind are there?
105 one-rupee, 126 fifty-paise and 168 twenty-five-paise coins. Take counts 5x, 6x, 8x. Their value is 5x + 3x + 2x = 10x rupees = 210, so x = 21.
Explain it simply
The ratio here is of the number of coins, not their value. A 50-paise coin is worth half a rupee, so 6x such coins are worth 3x rupees. Convert each count into rupees, add, and set the total equal to ₹210. This "count ratio versus value ratio" trap appears often in placement tests.
Example
Question: Coins of ₹1, 50 p and 25 p in the ratio 5 : 6 : 8 by number; total ₹210.
- Counts: 5x, 6x, 8x.
- Values in rupees: 5x x 1 = 5x; 6x x 0.5 = 3x; 8x x 0.25 = 2x.
- Total value = 10x = 210, so x = 21.
- Coins: ₹1: 105, 50 p: 126, 25 p: 168.
Check: 105 + 63 + 42 = ₹210.
The value ratio is 5 : 3 : 2, which is different from the count ratio 5 : 6 : 8.
const x = 210 / (5 * 1 + 6 * 0.5 + 8 * 0.25);
console.log([5 * x, 6 * x, 8 * x]); // Output: [105,126,168]What to say in the interview
"The ratio is by number of coins, so I convert to value: 5x, 3x and 2x rupees, totalling 10x. That's 210, so x is 21, giving 105, 126 and 168 coins."
Common mistakes
- Dividing ₹210 directly in the ratio 5 : 6 : 8, which treats it as a value ratio.
- Forgetting to convert paise to rupees.