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A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for B alone to paint the house?

A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for B alone to paint the house? Correct Answer 96

Let the total work = 48 (LCM of 48 and 16)

⇒ The efficiency of C = 48/48 = 1

⇒ The efficiency of (A + B + C) = 48/16 = 3

A is thrice as good a workman as B, the efficiency of A will be three times of the efficiency of B.

Let efficiency of B be p then efficiency of A will be 3p,

⇒ 3p + p + 1 = 3

⇒ 4p = 2

⇒ p = ½

⇒ Efficiency of B = ½

∴ Time taken by B alone to paint the house = 48/(½) = 96 days

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