Question : A, B, and C can do a job working alone in 50, 75 and 20 days, respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?
Option 1: 20
Option 2: 30
Option 3: 18
Option 4: 24
Correct Answer: 20
Solution :
Given:
A, B, and C can do a job working alone for 50, 75 and 20 days, respectively.
Total work = LCM of (50, 75, 20) = 300 units
Efficiency of A = $\frac{300}{50}=6$
Efficiency of B = $\frac{300}{75}=4$
Efficiency of C = $\frac{300}{20}=15$
Total work they have done in the first 4 days.
= 4 × (6 + 4 + 15) = 100 units
Remaining work = 300 – 100 = 200 units
Therefore, days required for A & B to complete the work
= $\frac{\text{Remaining work}}{\text{Efficiency of A and B combined}}$
= $\frac{200}{6+4}$
= $20$ days
Hence, the correct answer is 20.
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