Aptitude - Time and Work - Discussion

4 x+6y = 1/8 (I)
3x+7y=1/10.

32x+48y=1....(1)
30x+70y=1....(2)

2x-22y=0
X=11y

4*11y + 6y = 1/8
10y = 1/40.

I cannot understand this equation.
4x+6y=1/8.
3x+7y=1/10.

Please explain.

@All. The Shortcut method:

4m 6w =8days -> 1
3m 7w = 10day -> 2.

(4m+6w)8 = (3m+7w)10
32m+48w = 30m +70w
32m-30m = 70w-48w.

2m = 22w
1m = 11w ---> (3).

Substitute (3) in (1) or(2)

Eq(2)Converting men to women
(3m+7w)10.
((3*11w)+7w)10 = 10x.
40*10 = 10x.
x = 400/10.
x = 40.
Hope it is helpful.

Hi,

Could you please show me how did you compute to get x=11/400 & y = 1/400?

@All.

Please let me know.

How come x=11/400 and y=1/400?

Anybody explain.

Men=m, Women = w.

4m+6w = 1/8 so 32m + 48w = 1 ---> (1)
3m+7w = 1/10 so 30m + 70w = 1 ---> (2)

Now find the relation between m and w by equating 1 and 2.
We get m=11w.
Now put it in equation 1 we get;
4m+6w.
4*(11w)+6w.
50w complete work in 8 days.
10w complete work in (8*50)/10 = 40 days.

For this type of problem, we can use MDH/RW.

M = men, D = days, H = Hours , R = Rupees, W = work.

Note:- In this problem work is done by both men and women.
Total work is same so no need to write in the equation.

The modified formula would look like,
(M + W) x D/W.

(3M + 7W) x 10 = ( 4M x 6W) x 8,
30M + 70W = 32M + 48W,
70W - 48W = 32M - 30M,
22W = 2M.

W/M = 2/22 = 1/11,

i.e women to men efficiency ratio is 1 : 11.
We need to calculate total work,

Total work = efficiency x time.
Total work =( 3x11 + 7x1) x 10 = 400.
Days taken by 10 women to complete the same work is;
400/10x1. Here 1 is the efficiency of women as we calculated earlier.

(4 Men + 6 Women)*8= work ----> (1) eqn.
(3 Men + 7 Women)*10= work ----> (2) eqn.

Equating eq. (1) &(1) we get,
32Men + 48 women = Work,
30Men + 70 women = work.

Arrange it in,
32men + 48women=30men + 70women
32-30 men = 70-48 women
2 men = 22 women
1 men = 22/2 women
1 men = 11 women.

Therefore, we get.
Men =11 , Women = 1.
Putting this values in eq. (1).

Therefore,
(4*11+6*1) *8 = work.
Work = 400.

Now,
We know that 10 women's can do the work.

Therefore,
400 work = 10 women.
Work = 10/400 women.
Work = 1/40 women.

That means,

10 women complete the work in 40 days.

How to solve these two equations?

You are wrong @Kishor,

Right, Agree with you @Nagu.