A money bag contains one rupee, 5 rupee and 10 rupee coins in the ratio of 3 : 5 : 7 respectively. If the total amount in the bag is ₹980,then find the number of coins of ₹10.
- (a)71
- (b)68
- (c)69
- (d)70
Answer
Why
Correct — D. Let the counts be 3x, 5x and 7x for the ₹1, ₹5 and ₹10 coins.
Convert each count into rupees:
₹1 coins: 3x × 1 = 3x
₹5 coins: 5x × 5 = 25x
₹10 coins: 7x × 10 = 70x
Total value: 3x + 25x + 70x = 98x, and 98x = 980 gives x = 10.
Number of ₹10 coins = 7x = 7 × 10 = 70 → option (d).
Why the others are wrong
- (a)71 — 71 is not a multiple of 7, so it cannot equal 7x for any whole x. The 3 : 5 : 7 ratio forces the count of ₹10 coins to divide by 7.
- (b)68 — 68 would need x = 68⁄7, which would leave the ₹1 and ₹5 counts fractional as well. Coins cannot be split into parts.
- (c)69 — 69 is a near miss set one below the answer. The equation 98x = 980 is exact, giving x = 10 and 7x = 70, with no rounding anywhere in the working.
Concept
A ratio of coin counts is not a ratio of value. Multiply each count by its denomination first: 3x one-rupee coins are worth 3x rupees, but 7x ten-rupee coins are worth 70x rupees.
So the value ratio is 3 : 25 : 70, not 3 : 5 : 7. Adding those gives the single equation 98x = 980. The ₹10 coins are only 7 of the 15 parts by count, yet they carry ₹700 of the ₹980.
The bag holds 3x + 5x + 7x = 15x = 150 coins altogether. The question asks for a number of coins, not an amount of money, so the working stops at 7x = 70 rather than at 70x = ₹700.
Key facts
- For coins, value = count × denomination, so a 3 : 5 : 7 count ratio becomes a 3 : 25 : 70 value ratio.
- 98x = 980 gives x = 10, so the bag holds 30 one-rupee, 50 five-rupee and 70 ten-rupee coins.
- Those 150 coins are worth 30 + 250 + 700 = ₹980, which checks the answer.
- Only a multiple of 7 can be the count of ₹10 coins, and 70 is the one option that qualifies.
Study next
Common traps
- Splitting ₹980 in the ratio 3 : 5 : 7, which gives 7⁄15 × 980 = ₹457.33 and no whole count.
- Answering 700, the rupee value of the ₹10 coins, instead of their number.
- Forgetting that x must be a whole number, which alone rules out 71, 68 and 69.
This item hands you a ratio of counts. The same topic is also set from a fixed total number of coins, which changes the equation but not the method.
Compare 9 Sep 2024, 09:00, Quant Q.9, where ₹100 is paid with 40 coins of ₹5, ₹2 and ₹1, and 12 Sep 2024, 09:00, Quant Q.20, where ₹120 is paid with 25 coins of ₹10, ₹5 and ₹2.
Related PYQs
No directly related past PYQ was found.