A and B working together can complete a work in d days Working alone A takes 8 d days and B takes 18...........

Quantitative Aptitude (CGL) Time and work

A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B takes (18 + d) days to

complete the same work. A works for 4 days. The remaining work will be completed by B alone, in:

This questions was previously asked in

SSC CGL 4th March 2020 Shift-2

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24 days

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Explanation:

To find the time when A and B, working together = $\sqrt{more days taken by A \times more days taken by B}$
d = $$\sqr{8 \times 18}$$ = 12
Time taken by A to complete the work = (8 + d) = 8 + 12 = 20
Time taken by B to complete the work = (18 + d) = 18 + 12 = 30
Let the total work be 60.
(LCM of 20 and 30 is 60.)
Efficiency of A = 60/20 = 3
Efficiency of B = 60/30 = 2
Work done by A in 4 days = efficiency $$\times time = 3 \times 4 = 12$$
Remaining work = 60 - 12 = 48
Time taken by B to complete the remaining work = 48/2 = 24 days
$$\therefore$$ The remaining work will be completed by B alone, in 24 days.