2 boys and 5 girls can finish a piece of work in 4 days. 4 boys and 4 girls can finish the same work in 3 days. If a girl paid rs 750 each day, what may be the expenditure to complete the work?
Tomorrow is my test and I don't know how to solve this question. Someone please help!!!
I meant 'if a girl is paid rs 750......'
To solve this problem, we can break it down into two parts: the number of workers and the time it takes to complete the work.
Let's start with the number of workers. We are given that 2 boys and 5 girls can finish the work in 4 days, and 4 boys and 4 girls can finish it in 3 days. Let's assume that the work rate for a boy is B units per day and the work rate for a girl is G units per day.
Using this assumption, we can set up two equations based on the given information:
Equation 1: (2B + 5G) * 4 = 1 (the work is completed)
Equation 2: (4B + 4G) * 3 = 1 (the work is completed)
Now, let's solve these equations:
Equation 1: 8B + 20G = 1
Equation 2: 12B + 12G = 1
To solve this system of equations, we can use the method of elimination. Multiply Equation 1 by 3, and Equation 2 by 2 to eliminate the B terms:
Equation 1: 24B + 60G = 3
Equation 2: 24B + 24G = 2
Subtract Equation 2 from Equation 1:
36G = 1
G = 1/36 = 0.0278 (approximately)
Now that we have the value of G, we can substitute it into Equation 1 to find the value of B:
8B + 20(0.0278) = 1
8B + 0.556 = 1
8B = 1 - 0.556
8B = 0.444
B = 0.444/8
B = 0.0555 (approximately)
Now that we have the work rate per person, we can calculate how much work can be done in a day by multiplying the work rate by the number of workers:
Total work per day = (2B + 5G)
Substituting the values of B and G:
Total work per day = (2 * 0.0555) + (5 * 0.0278)
Total work per day = 0.111 + 0.139
Total work per day = 0.25 (approximately)
To calculate the total expenditure to complete the work, we need to multiply the total work per day by the number of days and the cost per day:
Expenditure = Total work per day * Number of days * Cost per day
Expenditure = 0.25 * 4 * 750 (since it takes 4 days to complete the work and the cost per day is Rs 750)
Expenditure = Rs 750 (approximately)
Therefore, the expenditure to complete the work is approximately Rs 750.
Note: It's always a good practice to double-check your calculations and assumptions to ensure accuracy.