(Q) 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, find the time taken by B to finish the work.

Ans:  Let’s assume B alone takes X days to finish the work.

(Note: Here, we take X for B because we need to find time taken by B)

Therefore, A alone can finish it in (X – 6) days.

(Note: it was given that A takes 6 days less than B)

Therefore, A’s one day’s work =

and B’s one day’s work =

Next, it is given that A + B, both together finish the work in 4 days,

Hence, (A + B)’s one day’s work =

Now, work done by A in a day and work done by B in a day will be equal to work done by both in a day.

therefore, (A’s one day’s work) + (B’s one day’s work) = (A + B)’s one day’s work

Lets put the values:

Here we reject X = 2 because if X = 2, X – 6 will be – 4 but number of days can not be negative,

Therefore, X 2 and only X =12.

Hence, B alone can finish the work in 12 days.

Check:

If B can finish the work in 12 days, his one days’ work is

A will finish the work in 12 – 6 i.e. 6 days, hence his one days’ work is

Now = one day’s work together

Since, here both finish the work in 4 days, hence our answer is correct.

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