Question : A and B can do a piece of work in 36 days. B and C can do the same work in 60 days. A and C can do the same work in 45 days. In how many days can A alone complete the same work?
Option 1: 90
Option 2: 60
Option 3: 120
Option 4: 45
Correct Answer: 90
Solution :
According to the question,
Let the total Work = LCM of 36, 60 and 45 = 180
The efficiency of (A + B) = $\frac{180}{36}$ = 5 units/day
The efficiency of (B + C) = $\frac{180}{60}$ = 3 units/day
The efficiency of (C + A) = $\frac{180}{45}$ = 4 units/day
Now,
⇒ 2 × efficiency of ( A + B + C ) = 5 + 3 + 4
⇒ The efficiency of ( A + B + C ) = $\frac{12}{2}$
So, efficiency of B = 6 – 4 = 2 units/day
⇒ The time taken by B = $\frac{180}{2}$ = 90 days
Hence, the correct answer is 90.
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