Aptitude - Time and Work - Discussion

Easiest way:

We want only 10 women value right so just take equation like:

4m + 6w = 1/8.....(1) *3.

3m + 7w = 1/10......(2) *4.

We get -10w = 3/8 - 2/5.

Solve w = 1/400.

So 10 women = (1/400*10) = 40.

Please learn how solve this equations?

Hi, Here I'm solving the equation in detail.


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

Now we need to cancel one term. Choose either x or y. I chose x. So I'll multiply equation 1 with 3 and equation 2 with 4.

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

The new values will be:

12x + 18y= 3/8 ----------> (1)
12x + 28y= 4/10 --------> (2)

Now subtract 1 from 2.

12x - 12x will be 0.

18y - 28y = -10y.

3/8 - 4/10 = -1/40.
So, -10y = -1/40.

y = -1/40/-10

y =1/400

Now Put the value of y in equation 1 or 2. I choose 1.

So, 4x + 6*1/400 = 1/8.

= 4x + 6/400 = 1/8.

= 4x = 1/8 - 6/400.

= 4x = 11/100.

x = 11/100/4.

=11/400.

So x = 11/400 and y= 1/400.

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.

Why we use days in fraction?

Please explain it in units method.

4x + 6y = 1/8 and 3x + 7y = 1/10.

How to get x = 11/400 why = 1/400 please explain me.

In simple way,

4 Man & 6 women complete works in 8 days i.e, 4M+6W=8....(1)
Similarly, 3M+7W=10......(2)
Solve both equations, (4M+6W)*8=(3M+7W)*10, i.e M/W=11/1

According to Qusetion.
Same work done by 10 Women.
(3M+7W)*10=10W * D.
Now put the values of M & W.
(3*11+7*1)*10=10 * 1 D.
33+7=D , i.e = 40.

I can't understand this solution. Anyone help me to get it.

Thanks for the complete solutions.