# T&W q3

### 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 8/23 of the work. How much should ajay be paid?​

Wa = Work Done per day by ajay
Wv =Work Done ,, by vijay
Ws= Work Done by sanjay

(Wa + Wv) * x1 = 19/23

(Wv + Ws) * x2 = 8/23

Total work they're doing = 27/ 23 which is over 1 whole work ? 1 work = 23/23

Give some hint ?

#### Dr.Peterson

##### Elite Member
Wa = Work Done per day by ajay
Wv =Work Done ,, by vijay
Ws= Work Done by sanjay

(Wa + Wv) * x1 = 19/23

(Wv + Ws) * x2 = 8/23

Total work they're doing = 27/ 23 which is over 1 whole work ? 1 work = 23/23

Give some hint ?
How are you defining x1 and x2??

If A, V, and S are the fractions of the work done by each, then A + V = 19/23 and V + S = 8/23. There's a third equation you can write, and then solve for the three variables. (Don't forget to answer the question, though!)

If T&W means Time and Work, then this is not that kind of problem; time is not involved. It's just a very basic algebra problem (or less). You can solve it without any algebra at all if you just observe that any work not done by Vijay and Sanjay must be done by Ajay.

#### HallsofIvy

##### Elite Member
Yes, of course 19/23+ 8/23= 27/23 is greater than 1. Part of the time all 3 people were working together and that time is counted in both times. We can say that 27/23- 1= 27/23- 23/23= 4/23 all three people were working together. 19/23- 4/23= 15/23 of the time, Ajay and Vijay only were working, 8/23- 4/23= 4/23 of the time Vijay and Sanjay ony were working together, and 4/23 of the time all three were woring together.

So Ajay was working for 15/23+ 4/23= 19/23 of the time, Vijay was working for 4/23+ 4/23= 8/23 and Sanjay was working for 4/23+ 4/23= 8/23 of the time.

Now, to distribute the pay we need to distribute the time. Those three fractions add to 19/23+ 8/23+ 8/23= 35/23. (19/23)/(35/23)=19/35 and (8/23)/(35/23)= 8/35. Of course, 19/35+ 8/35+ 8/35= 35/35= 1.

Ajay should receive (19/35)(Rs. 529)= Rs 287.17. Vijay should receive (8/35)(Rs. 529)= Rs 120.91. Sanjay should also receive (8/35)(Rs. 529)= Rs 120.91.

(That adds to 287.17+ 120.91+ 120.91= Rs 528.99. The missing Rs 0.01 is due to round off error. Assign it to anyone of the amounts.)

### 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?