Question

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

• A. 20
• B. 42
• C. 66
• D. None of Above

Answer 1

Answer: (B)

42

Answer 2

Let, the number of coins collected by $A$ and $B$ in one week as $3x$ and $4x$ respectively.
The total number of coins collected by $A$ in $5$ weeks $=15x$
For $15x$ to be a multiple of $7$, $x$ must be a multiple of $7$.
Similarly, the total number of coins collected by $B$ in $3$ weeks $=12x$
For $12x$ to be a multiple of $24$, $x$ must be a multiple of $2$.
Thus, $x$ must be a multiple of $7×2 = 14$
The minimum value for $x$ $=14$.
Therefore, the minimum number of coins collected by $A$ in one week $=3x = 3 × 14 = 42$.

So, the correct option is (B): $42$