The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is
Explanation:
Let the number of coins collected each week by A and B be 3x and 4x respectively.
For A: Coins collected by A in 5 weeks is a multiple of 7 ∴ 3x × 5 is a multiple of 7 ⇒ x is a multiple of 7.
For B: Coins collected by B in 3 weeks is a multiple of 24 ∴ 4x × 3 is a multiple of 24 ⇒ x is a multiple of 2.
∴ x is a multiple of 7 and 2, hence least possible value of x = 14.
⇒ Minimum possible number of coins collected by A in one week is = 3x = 42.
Hence, 42.
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