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?

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.