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

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Question :

Started 1 week ago by Shashank in

0 13

Answer : 42

Explanatory Answer

Let the number of coins collected by A and B in one week be 3x and 4x respectfully.
The total number of coins collected by A in 5 weeks = 15x
For 15x to be a multiple of 7, x has to be a multiple of 7.
The total number of coins collected by B in 3 weeks = 12x
For 12x to be a multiple of 24, x has to be a multiple of 2.
Therefore, x has to be a multiple of 7 × 2 = 14
The minimum value that x can take is 14.
So, the minimum coins collected by A in one week = 3x = 3 × 14 = 42.