Question : Working together, A and B can do a job in 40 days, B and C in 36 days, and all three together in 24 days. In how many days can B alone do the job?
Option 1: 60
Option 2: 90
Option 3: 72
Option 4: 120
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Correct Answer: 90
Solution :
Let the total work = LCM of (40, 36, and 24) = 360
Efficiency of (A + B) = $\frac{360}{40}$ = 9 ----------------------------(1)
Efficiency of (B + C) = $\frac{360}{36}$ = 10 --------------------------(2)
Efficiency of (A + B + C) = $\frac{360}{24}$ = 15 ---------------------(3)
Subtracting equation (1) from (3), we get,
Efficiency of C = 15 – 9 = 6
From equation (2), we get:
Efficiency of B = 10 – 6 = 4
So, time taken by B to do the work alone = $\frac{360}{4}$ = 90 days
Hence, the correct answer is 90.
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