Time and Work Problem.

[karthik.sharma]

4 Men and 3 Women can finish a job in 6 days.5 Men and 7 Women can finish the same job in 4 days.How long will 1 man and 1 woman take to finish the job.?

a) 22(2/7) days
b) 25 (1/2) days
c) 5 (1/7) days
d) 12 (7/22) days.

How do you solve such a problem?

[Rahul@gurome]

One day work of (4M + 3W) is 1/6. So, the 1st equation is 4M + 3W = 1/6
One day work of (5M + 7W) is 1/4. So, the 2nd equation is 5M + 7W = 1/4
Solving the equations by elimination method, we get W = 1/78 and M = 5/156
So, one day work of 1W + 1M = 1/78 + 5/156 = 7/156
Therefore, 1 man and 1 woman would take 156/7 or 22(2/7) days to finish the job.

[spoiler]The correct answer is (A).[/spoiler]

[gmatmachoman]

One day work of (4M + 3W) is 1/6. So, the 1st equation is 4M + 3W = 1/6
One day work of (5M + 7W) is 1/4. So, the 2nd equation is 5M + 7W = 1/4
Solving the equations by elimination method, we get W = 1/78 and M = 5/156
So, one day work of 1W + 1M = 1/78 + 5/156 = 7/156
Therefore, 1 man and 1 woman would take 156/7 or 22(2/7) days to finish the job.

[spoiler]The correct answer is (A).[/spoiler]

Rahul, seems a bit of calculation is invloved..will this much calculation is necessary in GMAT ?? Will these types pop up?

[frank1]

One day work of (4M + 3W) is 1/6. So, the 1st equation is 4M + 3W = 1/6
One day work of (5M + 7W) is 1/4. So, the 2nd equation is 5M + 7W = 1/4
Solving the equations by elimination method, we get W = 1/78 and M = 5/156
So, one day work of 1W + 1M = 1/78 + 5/156 = 7/156
Therefore, 1 man and 1 woman would take 156/7 or 22(2/7) days to finish the job.

[spoiler]The correct answer is (A).[/spoiler]

thanks
lol i was panicking for nothing...and was trying to solve it with arithmetic only....and was making problem unnecessarily big....
introduction of alzebra turned it into very simple problem...
may be this is good gmat question

thanks