A person has only ₹1 and ₹2 coins. The total number of coins is 50 and the total amount is ₹75. Find the number of ₹1 coins and ₹2 coins, respectively.
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A15 and 35
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B35 and 15
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C30 and 20
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D25 and 25
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E20 and 30
Answer
Correct Answer: 25 and 25
Explanation
Introduction / Context:Classic coin-count problems involve two variables: the number of lower-denomination coins and higher-denomination coins. You are given both the total count of coins and the total monetary value, which leads to a solvable system of linear equations.
Given Data / Assumptions:
- Total coins = 50.
- Total value = ₹75.
- Only denominations used are ₹1 and ₹2 coins.
Concept / Approach:Let x be the count of ₹1 coins and y be the count of ₹2 coins. Then x + y = 50 (count equation) and x + 2y = 75 (value equation). Solve simultaneously to get x and y in integers consistent with the constraints.
Step-by-Step Solution:
x + y = 50 … (1)x + 2y = 75 … (2)Subtract (1) from (2): (x + 2y) − (x + y) = 75 − 50 ⇒ y = 25.From (1): x + 25 = 50 ⇒ x = 25.Verification / Alternative check:Total amount = 25*₹1 + 25*₹2 = 25 + 50 = ₹75; total coins = 25 + 25 = 50. Both conditions satisfied.
Why Other Options Are Wrong:
- 15 and 35; 35 and 15; 30 and 20; 20 and 30: Each pair violates either the total coin count of 50 or the total value of ₹75 when tested.
Common Pitfalls:
- Mistakenly using 2x + y = 75 instead of x + 2y = 75 (mixing denominations).
- Not checking that both equations are satisfied simultaneously.
Final Answer:25 and 25