5. 3 men and 5 women can do a piece of work in 18 days. While 4 men and 9 women can do the same work in 12 days. If a man gets Rs.60 per day. What should be the wage per day of women?

To solve this problem, we need to establish a relationship between the work done by men and women.

Step 1: Let's denote the amount of work a man can do in a day as 'm' and the amount of work a woman can do in a day as 'w'.

Step 2: From the problem, we know that 3 men and 5 women can complete the work in 18 days. This can be written as: 3m + 5w = 1/18 (since the total work is considered as '1')

Step 3: Similarly, we know that 4 men and 9 women can complete the work in 12 days. This can be written as: 4m + 9w = 1/12

Step 4: Now we have a system of two equations, and we can solve it to find the values of 'm' and 'w'.

Step 5: Multiply the first equation by 4 and the second by 3, we get: 12m + 20w = 4/18 12m + 27w = 3/12

Step 6: Subtract the second equation from the first, we get: -7w = 1/18 - 1/4 -7w = -1/36 w = 1/36 * 1/7 w = 1/252

Step 7: Substitute w = 1/252 into the first equation: 3m + 5(1/252) = 1/18 3m = 1/18 - 5/252 3m = 7/252 m = 7/252 * 1/3 m = 7/756

Step 8: We know that a man gets Rs.60 per day. So, the wage per day of women should be: w/m * Rs.60 = (1/252) / (7/756) * 60 = Rs.20

So, the wage per day of women should be Rs.20.