CAPF AC 2022 Q45: General Mental Ability – Quantitative Aptitude
A person has a total of 100 coins consisting of ₹2 and ₹5 coins. If the total value of the coins is ₹320, then the number of ₹2 coins is
- (a) 40
- (b) 50
- (c) 60
- (d) 70
Answer: (c) 60
Explanation
Counting ₹2 and ₹5 coins
Given: 100 coins of ₹2 and ₹5 have a total value of ₹320; find the number of ₹2 coins.
How to think: suppose all 100 coins were ₹5 coins.
The value would be ₹500.
Each ₹5 coin swapped for a ₹2 coin reduces the value by ₹3.
| Step | Working |
|---|---|
| If all were ₹5 coins | 100 × 5 = ₹500 |
| Actual value | ₹320 |
| Excess | 500 − 320 = ₹180 |
| Fall per ₹2 coin | 5 − 2 = ₹3 |
| Number of ₹2 coins | 180 ÷ 3 = 60 |
Check: 60 × 2 = 120 and 40 × 5 = 200.
120 + 200 = 320.
Answer: (c) 60.
Why each option is right or wrong
- (a) Incorrect. 40 is the number of ₹5 coins, not ₹2 coins.
- (b) Incorrect. 50 of each would be worth ₹350, not ₹320.
- (c) CORRECT. 60 coins of ₹2 and 40 coins of ₹5 make ₹320.
- (d) Incorrect. 70 coins of ₹2 and 30 of ₹5 would be worth ₹290.
Key point
Two kinds of coins: assume all are of one kind, find the excess or shortfall, divide by the difference in value. Or solve x + y = 100 and 2x + 5y = 320.
Remember
All-₹5 trick: (500 − 320) ÷ 3 = 60.
Common mistakes
- Giving the number of ₹5 coins (40) when the question asks for ₹2 coins.
- Dividing ₹320 by 7, the sum of the two coin values.
- Making an error in sign when solving the two equations.
Exam tip
Educated guess: test the middle option first. 50 and 50 give ₹350, which is too high, so there must be more of the cheaper coin. Try 60: it gives ₹320.
Sources
- NCERT Class X Mathematics — Pair of Linear Equations in Two Variables
- NCERT Class VIII Mathematics — Linear Equations in One Variable (coin problems)