### Ajay, Vijay and Sanjay are employed to do a piece of work for rs.529. Ajay and Vijay together are supposed to do 19/23 of the work and Vijay and Sanjay together do 8/23 of the work. How much should Ajay be paid?

It looks like I need to be complete.

**The problem doesn't mention time at all**; it doesn't say that two of them are working together for part of the time, and so on, but only how much of the work each pair does. We must not confuse this with those time-worked problems.

If Vijay and Sanjay together do 8/23 of the work (that is, the sum of the amounts each one does is 8/23), then Ajay must do the rest of the work (since we have to assume that the work got done, or there's no way to answer the question). So Ajay did 1 - 8/23 = 15/23 of the work, and is paid 15/23 of the rs. 529, which comes to rs. 345.

Similarly, the fact that (A+V) + (V+S) = 27/23, which is more than 1, tells us that Vijay's work, which is counted twice, accounts for the overage, 4/23 of the work. And Sanjay does 8/23 - 4/23 = 4/23 of the work.

This checks out, because together Ajay and Vijay do 15/23 + 4/23 = 19/23, and Vijay and Sanjay do 4/23 + 4/23 = 8/23 as required.

@Saumyojit, were you given an answer we can compare with this to confirm my interpretation of the problem?