Maths-

General

Easy

Question

# If 5 men or 9 women can do a piece of work in 19 days then in how many days will 3 men and 6 women do the same work?

Hint:

**Hint:**

In a proportional relationship, the variables are related by a constant ratio(k). For example, the equation which can relate the two variables can be written in the form:

y = (constant) x or y = k x.

So, for solving these types of questions we need to create a proportional relationship between the variables. These relationships can be direct, inverse etc.

## The correct answer is: 15 days

### Step 1 of 3:

It is given that 5 men can do a piece of work in 19 days and 9 women can do the same piece of work in 19 days. Let’s say the total work done is W and let’s say that the work done by one man is x and the work done by one woman is y. So we can say that

5x = W ……..(1)

and 9y = W ………(2)

Equating equations (1) and (2)

5x = 9y

y = ………(3)

Step 2 of 3:

Now we are asked to determine the days that will be taken by 3 men and 6 women to do the same work. So we can say that

3x + 6y = W

From equation (3)

3x + 6 = W

3x + = W

= W

So, we can say that we need to find the number of days taken by men to complete the work

Step 3 of 3:

Let the number of days be represented as x and the number of men be represented as y. The number of men will increase if the number of days are decreased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as

y = ……..(4)

We now that 5 man can do a piece of work in 19 days i.e x = 19 and y = 5. Putting the values in equation (4)

5 =

k = 95

We need to find the no. of days taken by men. So,

=

Put the value of k = 95

=

x = 15 days

Final Answer:

Hence, 15 days are taken by 3 men and 6 women to do the same work.

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