A alone can finish a work in X days. B alone can finish the same work in X+5 day

Question

A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X

Options:

A . 12

B . 8

C . 10

D . 9

Answer: Option C
PART OF WORK COMPLETED BY A IN A DAY = 1/X PART OF WORK COMPLETED BY B IN A DAY
= 1/(X+5) (1/X)+(1/(X+5)) = 1/6 (2X+5)/(X²+5X) = 1/6 X²+5X = 6(2X+5) X²-7X-30=0 SOLVING, X=10

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