# A and B can together complete a work in 6 days .If A works alone for 2 days and complete 1/4 th of the work , in how many days B alone complete the remaining work?

If A?s 1 day?s work = 1/n, then A can complete the task in ?n? days.

In the problem, let A?s 1 day?s work = x

and let B?s 1 day?s work = y ?

It is given that A and B together can complete a task in 6 days?

So, 1 day?s work of A and B together

=>x + y=1/6?( Equation 1 )

Now it is also given that A can complete the task alone in 10 days?

So, A?s 1 day?s work = x = 1/10?

=>x = 1/10?( Equation 2 )

Now, putting the value of x from Equation 2 in Equation 1, we get

(1/10)+y=1/6

=>y = (1/6)?(1/10)

=>y = (10?6)/60

=>y = 4/60

=>y = 1/15

So, B?s 1 day?s work = 1/15(? y = B?s 1 day?s work)

Hence, B can complete the task in 15 days?

**
**