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work problem

by ankurmit » Mon May 30, 2011 10:23 pm
4 men and 3 women finish a job in 6 days, 5 men and 7 women can do the same job in 4 days. How long with 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
(e) 21 (3/7) days.
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by Frankenstein » Mon May 30, 2011 10:31 pm
Hi,
Let P be the total amount of work required to finish the job. Assuming all men are equally efficient with work rate 'm' and all women are equally efficient with work rate 'w'.
we get 4m + 3w = P/6 ->eqn(1)
5m + 7w = P/4 ->eqn(2)
Multiplying eqn(1) by 2 and adding to it eqn(2), we get 13m+13w=7P/12.
So m+w=7P/(13.12) = 7P/156.
So 1 man and 1 woman will take 156/7= 22(2/7) days to finish the job.
Hence, answer A

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by sivaelectric » Mon May 30, 2011 10:44 pm
Good explanation frankenstein :) is there any other precedure
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

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by manpsingh87 » Mon May 30, 2011 11:55 pm
ankurmit wrote:4 men and 3 women finish a job in 6 days, 5 men and 7 women can do the same job in 4 days. How long with 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
(e) 21 (3/7) days.
let work be 24 units; and m be amount of unit done by men per day and w be amount of unit done by women per day;

(24/4m)+(24/3w)=6;
(1/m)+(4/3w)=1;-----------1)
also;
(24/5m)+(24/3w)=4;
(6/5m)+(2/w)=1;------------2)

subtracting 1 and 2 we have;
1/5m=2/3w;
3w=10m;
w=(10/3)m;
put w=10/3 in 1 we have;
1/m+2/5m=1;
7/5m=1;
m=7/5;
therefore w=(10/3)*7/5=14/3;

hence no. of days taken by 1 men and 1 women to do the 24 units of work will be;
24/(7/5)+24/(14/3)=156/7= 22(2/7);

hence A
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by sivaelectric » Tue May 31, 2011 12:55 am
Great explanation :)
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

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by ankurmit » Tue May 31, 2011 8:29 am
Frankenstein wrote:Hi,
Let P be the total amount of work required to finish the job. Assuming all men are equally efficient with work rate 'm' and all women are equally efficient with work rate 'w'.
we get 4m + 3w = P/6 ->eqn(1)
5m + 7w = P/4 ->eqn(2)
Multiplying eqn(1) by 2 and adding to it eqn(2), we get 13m+13w=7P/12.
So m+w=7P/(13.12) = 7P/156.
So 1 man and 1 woman will take 156/7= 22(2/7) days to finish the job.
Hence, answer [spoiler]A[/spoile

Cheers!
Thanks dear.I was not able to solve these 2 equations.

How you got idea to multiply them and than adding it?
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by Frankenstein » Tue May 31, 2011 9:06 am
ankurmit wrote:
Frankenstein wrote:Hi,
Let P be the total amount of work required to finish the job. Assuming all men are equally efficient with work rate 'm' and all women are equally efficient with work rate 'w'.
we get 4m + 3w = P/6 ->eqn(1)
5m + 7w = P/4 ->eqn(2)
Multiplying eqn(1) by 2 and adding to it eqn(2), we get 13m+13w=7P/12.
So m+w=7P/(13.12) = 7P/156.
So 1 man and 1 woman will take 156/7= 22(2/7) days to finish the job.
Hence, answer [spoiler]A[/spoile

Cheers!
Thanks dear.I was not able to solve these 2 equations.

How you got idea to multiply them and than adding it?
Hi,
we need the coefficient of m and w to be same as we need m+w. So, lets say we multiply eqn(1) by 't' and add to eqn(2). then we (4t+5) and (3t+7) as coefficients of m and w. So, we equate them to get the value of 't'
4t+5=3t+7 => t=2.

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by finites » Thu Jun 02, 2011 11:50 am
ankurmit wrote:
Frankenstein wrote:Hi,
Let P be the total amount of work required to finish the job. Assuming all men are equally efficient with work rate 'm' and all women are equally efficient with work rate 'w'.
we get 4m + 3w = P/6 ->eqn(1)
5m + 7w = P/4 ->eqn(2)
Multiplying eqn(1) by 2 and adding to it eqn(2), we get 13m+13w=7P/12.
So m+w=7P/(13.12) = 7P/156.
So 1 man and 1 woman will take 156/7= 22(2/7) days to finish the job.
Hence, answer [spoiler]A[/spoile

Cheers!
Thanks dear.I was not able to solve these 2 equations.

How you got idea to multiply them and than adding it?


Frankenstein is solving equation for finding the variables.

like we have 2 equations.
for eg :
x + 2y =8
x - 3y =7
2 equations and 2 variables.. find x and y.

hope it helps
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by finites » Thu Jun 02, 2011 12:27 pm
As Frankenstien said go till equations.. ie P is the total amount of work,

4m + 3w work for 6 days to make P amount of work
5m + 7w work for 4 days to make P amount of work..

for one day they will do P/(no of days) amount of work..

4m + 3w = P/6
5m + 7w = P/4

cant i solve for m and w with respect to P and then add m and w ?

above equations become

24m + 18w = P
20m + 28w = P

eqn 1 - 2

4m -10w = 0 ie 4m = 10w or m = 5/2w

substituting m in equation 24m + 18w = P
60w + 18w = P
ie 78w = P

w = P/78 one woman should work for 78 days to complete the work..
using m = 5/2w
m= 5/2 (P/78)

w + m = P/78 + (P/78)(5/2)
= (P/78)(1 + 5/2)
= (P/78)(7/2)
= P * 7/156

to make P amount of work 156/7(m+w) ie 22(2/7)
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by GMATGuruNY » Thu Jun 02, 2011 2:04 pm
ankurmit wrote:4 men and 3 women finish a job in 6 days, 5 men and 7 women can do the same job in 4 days. How long with 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
(e) 21 (3/7) days.
Let job = 12 units.

Time for 4 men and 3 women = 6 days.
Thus, rate for 4 men and 3 women = w/t = 12/6 = 2 units per day.
Thus, rate for 8 men and 6 women = 4 units per day.

Time for 5 men and 7 women = 4 days.
Thus, rate for 5 men and 7 women = w/t = 12/4 = 3 units per day.

Combining the rate for 8 men and 6 women with the rate for 5 men and 7 women:
Rate for 13 men and 13 women = 4+3 = 7 units per day.
Thus, rate for 1 man and 1 woman = 7/13 units per day.

Time for 1 man and 1 woman to complete the job = w/r = 12/(7/13) = 156/7 = 22 ² � ₇ days.

The correct answer is A.
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