Question : A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find how many days B alone can do the work.
Option 1: 90 days
Option 2: 100 days
Option 3: 80 days
Option 4: 75 days
Correct Answer: 90 days
Solution :
Given: A and B can do a piece of work in 18 days.
The work done by A and B in 1 day = $\frac{1}{18}$.
B and C together can do it in 30 days.
The work done by B and C in 1 day = $\frac{1}{30}$.
Total work = Time × Efficiency
The ratio of efficiency of A and C = $2k:k$
According to the question,
(A + B)'s efficiency – (B + C)'s efficiency = $2k – k$
⇒ $\frac{1}{18}–\frac{1}{30}=k$
⇒ $k=\frac{5–3}{90}$
⇒ $k=\frac{2}{90}$
⇒ $k=\frac{1}{45}$
The efficiency of A = $2k=\frac{2}{45}$.
The efficiency of B = $\frac{1}{18}–\frac{2}{45} = \frac{5–4}{90}=\frac{1}{90}$
⇒ B completes the work in 90 days.
Hence, the correct answer is 90 days.
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