Question : A is thrice as good a workman as B and together they can finish a work in 32 days. In how many days will B alone complete the same work?
Option 1: 96 days
Option 2: 104 days
Option 3: 112 days
Option 4: 128 days
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Correct Answer: 128 days
Solution :
Let A take $x$ days to complete the work.
Then, amount of the work completed by A in 1 day = $\frac{1}{x}$
Then B would take $3x$ days to complete the work.
Then, the amount of the work completed by B in 1 day = $\frac{1}{3x}$
Now, it is given that they complete the work together in 32 days.
⇒ $\frac{1}{x}+\frac{1}{3x}=\frac{1}{32}$
⇒ $\frac{3+1}{3x}=\frac{1}{32}$
⇒ $3x = 32 \times 4 = 128$
Hence, the correct answer is 128.
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