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Question

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, then B alone can finish it

A
in 12 days
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B
in 9 days
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C
in 10 days
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Solution

The correct option is A in 12 days
Suppose B alone can takesx days to finish the work.
Then A alone can finish it in (x6) days.
B's 1 day's work = 1x.
A's 1 day's work = 1x6.
(A+B)'s 1 day's work = 14
1x+1x6=14
x6+xx(x6)=14
8x24=x26x
x214x+24=0
x212x2x+24=0
(x12)(x2)=0
x=12 or x=2
But x cannot be less than 6.
x=12
Hence, B alone can finish the work in 12 days

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