# Mahesh has some apples. He gave half of the apples to Suresh but got 1 apple back from Suresh. Then he gave half of the apples available with him to D

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Mahesh has some apples. He gave half of the apples to Suresh but got 1 apple back from Suresh. Then he gave half of the apples available with him to Dinesh and got 1 apple back from him. Third time he repeated the same process with Harish. In the end, he was having the same number of apples which he had in the beginning. Number of apples he had in the beginning is
1. 4
2. 6
3. 8
4. None of these

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Correct Answer - Option 4 : None of these

Calculation:

Let the Mahesh number of apple is 2x.

The apple given to Suresh = x

The remaining apple on Mahesh after taking 1 apple from Suresh = x + 1

The apple given to Dinesh = (x + 1)/2

The remaining apple on Mahesh after taking 1 apple from Dinesh = (x + 1)/2 + 1

The apple given to Harish = 1/2[(x + 1)/2 + 1]

The remaining apple on Mahesh after taking 1 apple from Harish = 1/2[(x + 1)/2 + 1] + 1

According to the question;

⇒ 2x = 1/2[(x + 1)/2 + 1] + 1

⇒ 2x = (x + 1)/4 + 1/2 + 1

⇒ 2x = x/4 + 1/4 + 1/2 + 1

⇒ 2x - x/4 = 1/4 + 1/2 + 1

⇒ 7x/4 = 7/4

⇒ x = 1

The number of apple Mahesh has = 2 × 1 = 2

∴ The number of apple Mahesh had in beginning is 2