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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 255
Suppose she had x apples in the beginning.
Sold to the first customer =x2+12=x+12
Remaining stock =xx+12=2xx12=x12
Sold to the second customer =12×x12+12=x14+12=x1+24=x+14
Remaining stock =(x12)(x+14)=2x2x14=x34
Sold to the third customer 12×x34+12=x38+12=x3+48=x+18
Remaining sock =(x34)(x+18)=2x6x18=x78
Sold to the fourth cutomer =12×x78+12=x716+12=x7+816=x+116
Therefore, x[x+12+x+14+x+18+x+116]=15
x[8x+8+4x+4+2x+2+x+116]=15
x[15x+1516]=15
16x15x1516=15x15=16×15=240
x=240+15=255
Therefore, she had 255 apples before she stared selling.

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