Aptitude - Time and Work - Discussion

4m + 6w = 1/8 -------------------(1)
3m + 7w = 1/10 ------------------(2)

Then (1) *3 & (2)*4.

12m + 18w = 3/8 -------->(3)
12m + 28w = 4/10 ------> (4)

(4)-(3).
You will get 10w=1/40

Therefore, 40 days is the answer.

(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.

@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.

Given:

4m + 6w = 8 days ---> (1)
3m + 7w = 10 days ---> (2)

Total work = Efficiency × days.

By solving equation (1) and (2).
(4m + 6w) × 8 = (3m + 7w) × 10.
16m + 24w = 15m + 35w,
16m - 15m = 35w - 24w,
m = 11w.

Total work = (4 × 11 + 6) × 8.
Total work = 400 unit.
Time taken by 10 women = 400/10.
Time taken by 10 women = 40 days.

4m + 6w = 8 days.
3m + 7w = 10 days.
10w = Tdays.

4m + 6w = 1/8days --->(1)
3m + 7w = 1/10days ----> (2)
10w = Tdays ----> (3)

1st step is to find the value of m and w with (1)&(2)
32m + 48w = 30m + 70w.
32m - 30m = 70w - 48w.
m/w = 22/2.
m = 11 w = 1.

By product method;
(2)=(3).. you can also take (1) instead of (2).
mw*T = mw*T.
[3(11) + 7(1)] * 10 = 10 * T.
400 = 10T.
T = 40days.

4x+6y=1/8 ------> (1)
3x+7y=1/10 ----> (2).

Eqn 1 divided by 3.
Eqn 2 divided by 4.
12x+18y=3/8----(3).
12x+28y=4/10---(4).
-------------------------
-10y=1/40.
Y=1/40*10.
y=1/400.

Y value substitute in eqn (1).
4x+6(1/400) =1/8,
4x+6/400=1/8,
4x=1/8-6/400,
4x=44/400,
X=44/400*4,
X=11/400.

1 women complete a work=1/400*10.
1/40.
Hence, 10 women

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.

4m+6w=8 days.
3m+7w=10 days.
10w=?
(4m+6w)=1/8.
(3m+7w)=1/10.

Now,
32m + 48w = 30m + 70w.
2m = 22w
2/22 * m = Bawa
2/22 = w/m.
so, w=2 and m=22,
again,
(4m+6w)*8=(10w)*x.
(4*22+6*2)*8=(10*2)*x.
800=20x.
x=40 answer.

@All

Make an equation;
4m + 6w = 8d ---> 1
3m + 7w = 10d ---> 2

Step 2:
Eliminate or make RHS of both the Eqn equal ie:days
32m + 48w = 1d (divide RHS by 8 and multiply LHS by 8)
30m + 70w = 1d (same)

Step3: RHS = LHS( find the relationship of efficient b/w men and women)
32m + 48w = 30m + 70w
2m = 22w
1m = 11w.

Step4: put it in any eqn 1.
44w + 6w = 8d.
50w = 8d.
400w = 1d ..ie to finish the work in 1 day 400 women are needed.
Now to finish the work in 10 days,
400w = x * 10d (x is the amount of work),
x = 400/10 = 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.