If 5 men with 7 boys can earn Rs.127.50 in 6 days and 2 men with 3 boys can earn Rs.35 in 4 days, then find the time in which 7 men with 6 boys will earn Rs.750.

Let's solve this step by step:

Step 1: Let's assume the daily earnings of a man and a boy are Rs. m and Rs. b respectively.

Step 2: According to the first condition, 5 men and 7 boys earn Rs.127.50 in 6 days. So, their daily earnings would be Rs.127.50/6 = Rs.21.25. We can write this as: 5m + 7b = 21.25 ---- (Equation 1)

Step 3: According to the second condition, 2 men and 3 boys earn Rs.35 in 4 days. So, their daily earnings would be Rs.35/4 = Rs.8.75. We can write this as: 2m + 3b = 8.75 ---- (Equation 2)

Step 4: Now, we have two equations and two variables. We can solve these equations to find the values of m and b.

Step 5: Multiply Equation 1 by 2 and Equation 2 by 5, we get: 10m + 14b = 42.5 10m + 15b = 43.75

Subtract the second equation from the first, we get: -b = -1.25 So, b = 1.25

Step 6: Substitute b = 1.25 in Equation 1, we get: 5m + 7(1.25) = 21.25 5m + 8.75 = 21.25 5m = 21.25 - 8.75 5m = 12.5 So, m = 12.5/5 = 2.5

Step 7: Now, we know the daily earnings of a man (m = 2.5) and a boy (b = 1.25). We need to find out the time in which 7 men and 6 boys will earn Rs.750.

Step 8: The daily earnings of 7 men and 6 boys would be 7m + 6b = 7(2.5) + 6(1.25) = 17.5 + 7.5 = Rs.25

Step 9: Therefore, the time they would take to earn Rs.750 would be 750/25 = 30 days.

So, 7 men with 6 boys will earn Rs.750 in 30 days.