Aptitude - Time and Work - Discussion

Let,

1 man's 1 day's work = x.
so, 4 men's 1 day's work = 4x.

Let,
1 woman's 1 day's work = y.
so, 6 woman's 1 day's work = 6y.

Then
4 men's 6 woman's 1 day's work = 4x + 6y --------> (1)

Given,
4 men's 6 woman's 8 day's work = 1
So, 4 men's 6 women 1 day's work = 1/8 -----------> (2).

From 1 and 2,
4x + 6y = 1/8 ----------------------> (3)
According to (3)
3x + 7y = 1/10 ---------------------> (4)

Solving 3 and 4 we get,
10y = 1/40.
=> y = 1/400.
So, 1 woman's 1 day's work = 1/400.

Now,
1 woman's 1/400 work = 1 day,
1 woman's 1 work = 400 day,
10 woman's 1 work = 400/10 days,
= 40 days.
Ans : 40 days

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

Then We will get;
10y (women) = 1/40.
Ans. 40days.

1/8 * 3 = 3/8 not 1/24.

@All.

(4M+6W)8 = (3M+7W)10
32M+48W = 30M=70M
32M-30M + 48W-70W=0
2M-22W = 0
M = 11W.
Here one Man is equal to 11 Women.
Take 4m+6w to take 8 days equation.
4m=11 * 4w.
4M=44W==> 44W+6W =50.
50 women take 8 days.
10 Women's takes 8 * 5 = 40 days.

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

Multiply EQ(1)with 3,and EQ(2)with4, then,
12x+18y = 3/8.
12x+28y = 4/10.

Now, x terms get cancelled and then we have,
-10y = 3/8 - 4/10 from this step we got 10y = 40.

Hi,

Lets consider men =x , women =y;
Consider equation 1 is 4x+3y=1/8 ;
Consider equation 2 is 3x+7y=1/10;

Before solving above two equation ,
The first equation multiplied by 3,
The second equation multiplied by 4 for cancelling purpose.
After multiplying the equation 1 and 2 becomes,

12x+18y = 3/8.
12x+28y = 4/10.

By solving this above equation by sign change, we get,
-10y= -4/10 + 3/8.

Taking lcm in right and side, it will be;
-10y= (-32+30)/80;
-10y= -2/80:
Therefore y = 2/800 =1/400.

One women work = 1/400;=400 days.

Therefore 10 women work = 10 * 1/400 =1/40 = 40 days.

Thank you.

Can anyone solve the equation clearly?

Thanks @Chan and @Ashish.

(4m + 6w)x8 = (3m +7w)x 10.
2m =22w,
1m= 11w,
M/w = 11/1,

Put value
(3m + 7w) x 10.
(3x11 + 7x1) x10.
(33+7)x10.
400.
(10wx1)xd = 400.
D = 400/10.

40days.

8*(4M+6W) = 10*(3M+7).
32M + 48W = 30M + 70W,
32M - 30M = 70W - 48 W,
2M = 22W,
M = 22/2 W,
M= 11W,
IT MEANS 1 man = 11 women.

So, 4 Man = 4*11 = 44 Women,
Now, 44 + 6 = 50 Women.

Then 50 Women work done in 8 days...so those work 10 women compleat in how many days ?
So, 50*8/10 = 40 days.