Question : A can complete a task at the same time in which B and C work together. If A and B could complete it jointly in 10 days and C alone in 50 days, then B could complete it independently in:
Option 1: 26 days
Option 2: 27 days
Option 3: 25 days
Option 4: 23 days
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Correct Answer: 25 days
Solution :
(A + B)'s 1 day's work $= \frac{1}{10}$
C's 1 day's work $= \frac{1}{50}$
⇒ (A + B + C)'s 1 day's work $= \frac{1}{10} +\frac{1}{50}= \frac{6}{50} =\frac{3}{25}$ ............ (1)
A's 1 day's work = (B + C)'s 1 day's work .................. (2)
From (1) and (2) we get,
2 $\times$ (A's 1 day's work) $= \frac{3}{25}$
⇒ A's 1 day's work $= \frac{3}{50}$
⇒ B's 1 day's work $=\frac{1}{10} - \frac{3}{50} =\frac{1}{25}$
So, B can complete the work in 25 days.
Hence, the correct answer is 25 days.
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