Q) A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

a) 23 days                     b) 37 days             c) 37 1/2 days                     d) 40 days

Ans:

Time taken by A to do 80% work = 20 days

∴ Time taken by A to do full work = 20/80% = 25 days

Work completed by A = 80%

∴ Remaining work = 1 – 80% = 20%

∴ Time taken by (A + B) to finish 20% work = 3 days

∴ Time taken by (A + B) to do full work = 3/20% = 15 days

A’s 1 day work = 1/25

(A + B)’s 1 day work = 1/15

B’s 1 day’s work = (A + B)’s 1 day work  – A’s 1 day work  = 1/15 – 1/25 = 2/75

∴ Time taken by B to do full work = 1 / (2/75) = 75/2 = 37 1/2 days

Hence, Answer is [C].

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