So much work to do!
Kamal and Sandeep start doing a task, working alternatively for a day each. The tasks gets done in exactly 13 days when Kamal start the task on the first day. And it takes exactly days when Sandeep start the task on the first day. In how many days will the task be done, if both work together on the task?
If your answer is , where and are coprime positive integers, find .
The answer is 38.
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1 solution
We don't have to care about the first 1 2 days as in them same work is done in both the cases.
Lets assume :
One day work of K a m a l = K 1
One day work of S a n d e e p = S 1
First Case: K a m a l starts the work and the last one to finish is K a m a l only, work done by him = K 1 .
Second Case: S a n d e e p starts the work and the last one to finish is S a n d e e p only, with leaving one-third of the work which K a m a l can do in a day, Total work done= 3 K 1 + S 1 .
Both the work done are equal, Therefore:
K 1 = 3 K 1 + S 1
we get: K 1 = 2 S 3
From here we get, that K a m a l alone can finish the work in 1 1 days, while S a n d e e p alone can finish the work in 2 3 3 days.
They will finish the work together in X days X 1 = K 1 + S 1 = 1 1 1 + 3 3 2 = 3 3 5
So X = 5 3 3 = b a
a + b = 3 8