Question

I can do 2 / 3 of a certain work in 6 days and B can do 1 /4 of the same work in 3 days in how many days can both finish the work working together

Answer 1

Let me take I as A

Total work done is directly proportional to the time taken,

Now, A can do the 2/3 rd of work in 16 days
and B does 1/4 th work in 3 days.

Work done by A in one day = [2/3] / 16 = 2/ 16 * 3= 2/48 = 1/24
Work done by B in one day = [1/4] / 3 = 1/4*3 = 1/12.

So, the amount of work done in one day when both work together

= 1/24 + 1/12

= 1/24 + 2/24

= 3/24

= 1/8 

So, now time taken by both of them to do the work together

= 8 days

So, when both A and B work together then they finish the work in 8 days.

Hope this helps you !!!