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Question

Suppose A and B together can do a job in 12 days, while B alone can finish it in 30 days. In how many days can A alone finish the work?

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Solution

A can do a work in n days. Then A's one days work will be 1n.
Since A and B can do a job in 12 days,
1A+1B=1121
But B can finish the work in 30 days.
1B=1302
Substituting 2 in 1 we get
1A+130=112
Taking 130 on the right side
1A=112130

1A=5260 Taking LCM

1A=360

1A=120

Therefore A can alone finish the work in 20 days.

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