A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :8 days10 days12 days15 days
Question
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :8 days10 days12 days15 days
Solution
The first step is to determine the rate at which A and B can complete the work.
A can complete the work in 15 days, so A's rate is 1/15 of the work per day.
B can complete the work in 10 days, so B's rate is 1/10 of the work per day.
When A and B work together, they can complete 1/15 + 1/10 = 1/6 of the work per day.
They worked together for 2 days, so in those 2 days, they completed 2 * (1/6) = 1/3 of the work.
That means there is 1 - 1/3 = 2/3 of the work left.
A completes the work at a rate of 1/15 per day, so to complete 2/3 of the work, A would take (2/3) / (1/15) = 10 days.
So, the total time to complete the work is 2 days (when A and B were working together) + 10 days (when A was working alone) = 12 days.
So, the whole work was completed in 12 days.
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