Three men A, B, and C working together, complete a work in 10, 15, and 30 days respectively. If A and B left the work 4 days and 3 days respectively before the completion of the work, how many days in total did it take to finish the work?
Answers
Answer:6 Days
Step-by-step explanation:Three men A, B, and C complete the work in 10, 12, and 15 days. A and B left the work 2 days before the completion of the work, then the whole work will finish in how many days?
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Let W denotes the whole given work. It is mentioned that A, B & C individually complete the work W in 10, 12, and 15 days respectively. So in 1 day, A, B & C complete respectively amounts of work W/10, W/12 & W/15.
After A, B & C all started to work together, it is given that A & B left 2 days before the completion of the work and then C finished the remaining work. Let N denotes the number of days required to complete the whole work W. So we get the following equation,
(N - 2)*(W/10 + W/12 + W/15) + 2*(W/15) = W
or (N - 2)*(1/10 + 1/12 + 1/15) + 2/15 = 1 or (N - 2)*(13/60) = 1 - 2/15 = 13/15
or N - 2 = 4 or N = 6 (days) [Ans