time and work question how to solve this

Question

A,B,C are employed to do a piece of work for Rs 5290. A and B together are supposed to do 19/23 th of the work and B and C together 8/23 th of the work then A should be paid

A.Rs 4250

B.Rs 3450

C.Rs 1950

D.Rs 2290

sir can you tell me how to solve this

B and C together will do 8/23 of the work, so what part of the work will A do? Then the corresponding part of the whole payment shall be...? — CiaPan, Jul 09 '15 at 09:35
ans is right 3450. but can you explain that 15/23 how it come-- Michael Galuza — kuberkashyap, Jul 09 '15 at 09:38

score 1 · Answer 1 · answered Jul 09 '15 at 09:39

1

We're going to write $A,B,C$ for the fraction of the total work that each person does. We are given that $$A+B=\frac{19}{23}$$ $$B+C=\frac{8}{23}$$ And we finally impose $$A+B+C=1$$ as they must sum to 1. Really we only need the last 2 equations. We substitute the second into the 3rd to give $A+\frac{8}{23}=1$, i.e. $A=1-\frac{8}{23}=\frac{15}{23}$. So $A$ should be paid $\frac{15}{23}*5290=3450$

answered Jul 09 '15 at 09:39

Mar5bar

387

great. i am asked this qustion many frends of mine no body solve and explian but this explanation is great. – kuberkashyap Jul 09 '15 at 09:42

true blue anil · Accepted Answer · 2015-07-09T09:52:37.280

Have you reproduced the question exactly ? As it stands, it makes little sense.

However, interpreting that in a certain time, A and B working together can do 19/23 of the work, while B and C (in the same time) can do 8/23 of the work, we can write two equations

A + B = 19/23

B + C = 8/23

Adding the two, A + 2B + C = 27/23

Assuming that A,B and C together would just complete the work in the given time, B can complete only 27/23 - 23/23 = 4/23 of the work, and A can complete 19/23 - 4/23 = 15/23 of the work.

Thus A's pay should be $\frac{15}{23}\cdot 5290 =3450 $

time and work question how to solve this

2 Answers2