Question

# 2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days What is the time taken by 1 woman alone?

- 16 days
- 36 days
- 46 days
- none of these

Hint:

### A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign. We have to find the the time taken by 1 woman alone. Here we will create some equations and then find the values of the variables created.

## The correct answer is: 36 days

### Now here we have given that 2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days.

So let the number of days taken by a woman be x and the number of days taken by a man be y.

Then the equation becomes:

4(2/x + 5/y) = 1

2/x + 5/y = 1/4

3(3/x + 6/y) = 1

3/x + 6/y = 1/3

Now putting the expressions, 1/x = p and 1/y = q in these equations formed, we get:

2p + 5q = 1/4

Here we will do cross multiplication for simplification, we get:

p/-20 – (-18) = q/-9 – (-18)

1/144b- 180 ⇒ p/-2

q/-1 = 1/-36 ⇒ p/-2

– 1/36 and q/-1 = 1/-36

p = 1/18 and q = 1/36

p = 1/x = 1/18 and q = 1/y = 1/36

x = 18 and y = 36

So the total number of days taken by a woman is 18.

So here we used the substitution method to solve the question, apart from this method we can also use the elimination method to solve the problem as we have variables here. So the total number of days taken by a woman is 18.

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