Aptitude - Time and Work - Discussion

@All.

Please let me know.

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

Anybody explain.

Ok I didn't see all the example but I tried and found the following the easiest.

Men= x, Women= y.
So
(4x + 6y) will all the work in ? ans= 8 days (Given).

Then work done by (4x+6y) in 1 day = 1/8 (eq 1) simple, right ?).

Similarly we will get 3x+7y = 1/10... (eq 2).

Now if we can find out the amount of work done by 1 women (i.e - Y) then we can easily find out work done by 10 ?

2 eq

4x + 6 y = 1/8

3x + 7y = 1/10 Now think if we can eliminate X from the eq

Hmm.. Multiply eq 1 by 3 i.e 3* (4x + 6y = 1/8)

Multiply eq 2 by 4 i.e 4* (3x + 7y = 1/10)

We will get?

12x + 18y = 3/8.

12x + 28y = 4/10 or 12x + 28 y = 2/5 .

subtract them . X is gone :D

28y-18y = 2/5 - 3/8

=> 10y= 16-15/40

=> 10y= 1/40

=> y = 1/400 ( This is all we wanted ) .

1 women (i.e y ) can do 1/400 of work.

10 women will do in ? 10*1/400 = 1/40.

Actually 40 days! done.

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.

How to solve these two equations?

@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.

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.

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?