Aptitude - Time and Work - Discussion

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.

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.

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.

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

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.

Hi Poonam,

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
So 4 man's 1 day's work= 4x and 6 woman's 1 day's work = 6y.
Working together overall work will done in 8 days.
So working together overall work will done in 1 day = 1/8

i.e 4x + 6y = 1/8

So 3 man's 1 day's work= 3x and 7 woman's 1 day's work = 7y.
Working together overall work will done in 10 days.
So working together overall work will done in 1 day = 1/10

i.e 3x + 7y = 1/10

By solving
4x + 6y = 1/8 * 3
3x + 7y = 1/10 * 4
------------------------
12x + 18y = 3/8
12x + 28y =4/10

So 10y = 1/40

y= 1/400
x=11/400

(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

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.

4 men + 6 women = 8 days.
3 men + 7 women = 10 days.

10 women = ?

8(4 men + 6 women) = 10(3 men + 7 women).
32 men + 48 women = 30 men+70 women.

So 2 men = 22 women. Then 1 man = 11 women.

Now convert men into women. 4 men + 6 women = 8 days.

Now instead of 4 men write 44 women. So 44 women + 6 women = 8 days.

50 women ------- 8 days.
10 women -------- ?

m1 d1 = m2 d2.
50*8 = 10*?

So 10 women can do work in 40 days!

4 men and 6women can do the work in 8 days.
3 men and 7women can do that work in 10 days.
...........................................
So, 1men can be replaced by 1women with extra 2 days work.
4men can be replaced by 4 women with 2*4=8 extra days work.
Now total men worker '0' & total women workers 6+4=10,
This 10 women can do that work in 8+8(extra days) =16 days.
so, the answer should be 16 days.