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?
A) 20 B) 30 C) 18 D) 24
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"A can complete the job alone in 12 days, so A can complete 1/12 of the job in one day
"Similarly B and C can complete 1/18 and 1/36 of the job respectively.
"So if A, B and C work together for 2 days, then the amount of job completed will be 2(1/12 + 1/18 + 1/36) = 2(3/36 + 2/36 + 1/36) = 2(6/36) = 2/6 = 1/3 of the job.
"B quits and the amount of job left is 1 - 1/3 = 2/3
"So, let the no. of days taken by A and C to complete the rest of the job together be n
"Therefore n(3/36 + 1/36) = 2/3
"Or n(4/36) = 2/3
"Or n/9 = 2/3
"Or n= 2/3 × 9 = 2×3 = 6
"So, A and C will take 6 days to finish the rest of the job.
"HOPE IT HELPS
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