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X, Y and Z take 18 days to complete a piece of work. If X works alone he finishes the work in 36 days and if Y works alone he finishes it in 60 days. How long will it take Z to complete the work alone? A. 78 days B. 90 days C. 96 days D. 14 days

X, Y and Z take 18 days to complete a piece of work. If X works alone he finishes the work in 36 days and if Y works alone he finishes it in 60 days. How long will it take Z to complete the work alone? A. 78 days B. 90 days C. 96 days D. 14 days Correct Answer B

Suppose, Z will complete the work in = x days

According to the question,

1/36 + 1/60 + 1/x = 1/18

⇒ 1/x = 1/18 – 1/36 – 1/60

⇒ 1/x = (10 – 5 – 3)/180

⇒ 1/x = 1/90

⇒ x = 90

∴ Z will take 90 days to complete the work

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