GATE 2026 XH5 (Psychology) – Question 26
A man visits four relatives on a day. He purchases some sweets and gives a part of it to the first relative. Next, he purchases the same number of sweets he is left with after he visited his first relative. He repeats this process while visiting his other relatives. Finally, he gives all the sweets to his fourth relative. It is known that he gives equal number of sweets to all the relatives and is left with no sweets after the fourth relative. Assuming that he initially purchased more than 20 sweets, the minimum number of sweets he gave to each relative is _______________. (Answer in integer)
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Correct answer: 16
Explanation
Let him buy $n$ sweets first and give $x$ to each relative. After the first relative he has $n - x$, and buying the same number again makes it $2(n - x)$. After the second he has $2n - 3x$ and then doubles to $4n - 6x$. After the third he has $4n - 7x$ and doubles to $8n - 14x$. The fourth relative gets all of it, so $8n - 14x = x$, that is $8n = 15x$. So $n = 15k$ and $x = 8k$. With $n > 20$ the smallest choice is $k = 2$, giving $n = 30$ and $x = 16$.