Aptitude - Time and Work - Discussion

LCM METHOD:
LCM8, 10) = 40 units.

4M + 6W -> 8 days -> 5 units per day.
3M + 7W -> 10days -> 4 units per day.

3 * (4M + 6W) = 5 units per day -----> (1).
4 * (3M + 7W) = 4 units per day -----> (2).

Solving eq (1) and eq (2);

We get 10W =1 unit per day.

Therefore, 40 units/(1 unit per day) = 40 days.

(4m+6w)8 ---> (i)
(3m+7w)10 ---> (ii)

As per question.
(4m+6w)8=(3m+7w)10.

32m+48w=30m+70w.
2m=22w.
m/w=22/2 or 11/1.
Putting m=11 and w= 1 in eq(i)
(4*11+6*1)8 =400.

10 women complete work in 400/10 =40.

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.

How to solve these two equations?

@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.

@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.

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.

If 4 men and 6 women can complete a work in 8 days
4 men and 1 women can complete a work in=6* 8 days
1 men and 1 women can complete a work in=4*6* 8 days
1 men and 7 women can complete a work in=4*6*8/7 days
3 men and 7 women can complete a work in=4*6*8/(3*7) days
=64/7days
which is not 10 days as given in the question

How 1/40 become 40?

Hi Kishor,

you are wrong. This question is correct and the explanation is also correct.
Please refer once again.