Solution
Given:• Total number of apples with both of them = 80
• If Jill gives certain number of apples to Jack, then the number of apples with Jack = 4 * the number of apples with Jill
• If Jack gives the same number of apples to Jill, then the number of apples with Jack = 3 * the number of apples with Jill
To find:• The number of apples that jack has initially
Approach and Working: • Let us assume that the number of apples with Jack and Jill initially are P and Q
Now, when Jill gives x apples to Jack
• The number of apples with Jack will be = P + x, and
• The number of apples with Jill = Q – x
As per given information, P + x = 4(Q - x)
• Which implies that 4Q – P = 5x …………. (1)
And, when Jack gives x apples to Jill
• The number of apples with Jack will be = P - x, and
• The number of apples with Jill = Q + x
And we are given that P - x = 3(Q + x)
• Which implies that P - 3Q = 4x …………. (2)
Solving equations (1) and (2), we get,
Thus, P must be a multiple of 31, since x is an integer
• And, we know that P + Q < 80
• Implies, 31x + 9x < 80
• Thus, x < 2
Therefore, the only possible value of P = 31 * 1 = 31
Hence the correct answer is Option A.
Answer: A
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