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Question

# A woman sells to the first customer half of her stock of apples and half an apple, to the second customer she sells half her remaining stock and half an apple, and so on to the third and to the fourth customer. She finds that she has now 15 apples left. How many apples did she have before she started selling?

A
422
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B
375
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C
255
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D
182
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Solution

## The correct option is D 255Suppose she had x apples in the beginning. Sold to the first customer =x2+12=x+12Remaining stock =x−x+12=2x−x−12=x−12Sold to the second customer =12×x−12+12=x−14+12=x−1+24=x+14Remaining stock =(x−12)−(x+14)=2x−2−x−14=x−34Sold to the third customer 12×x−34+12=x−38+12=x−3+48=x+18Remaining sock =(x−34)−(x+18)=2x−6−x−18=x−78Sold to the fourth cutomer =12×x−78+12=x−716+12=x−7+816=x+116Therefore, x−[x+12+x+14+x+18+x+116]=15⇒x−[8x+8+4x+4+2x+2+x+116]=15⇒x−[15x+1516]=15⇒16x−15x−1516=15⇒x−15=16×15=240⇒x=240+15=255 Therefore, she had 255 apples before she stared selling.

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