Coins of three denominations — Aptitude Question
Coins of three denominations: A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in all. How many 50-paise coins are there?
Options
- 105
- 126
- 168
- 210
Show the answer and the worked solution
Correct answer: B. 126
Worked solution
- One set of coins is worth 5 × 1 + 6 × 0.50 + 8 × 0.25 = 5 + 3 + 2 = ₹10.
- Number of sets = 210 ÷ 10 = 21.
- 50-paise coins = 6 × 21 = 126.
Answer: 126.
The idea
When counts are in a ratio but the total is a value, price one complete set of the ratio and see how many sets the money buys. Converting the count ratio into a value ratio in the head is where mistakes creep in.
Shortcut. Turn counts into value: 5 × ₹1 : 6 × 50p : 8 × 25p = 5 : 3 : 2, so the 50-paise coins are worth 3/10 × ₹210 = ₹63, which is 126 coins.
Common trap. "105" — finding 21 sets but multiplying by the ₹1 coins' 5 instead of the 50-paise coins' 6.