If 14 men & 18 boys can do a piece of work in 6 days, and 15 men and 24boys can do it in 5 days, how long it will 10 men and 12 boys take to do it?
Answers
Answer:
It would take 10 men and 12 boys 10.8 days to complete the work.
Step-by-step explanation:
Let the amount of work be represented by W. Then, we can set up two equations based on the given information:
Equation 1: (14m + 18b) × 6 = W
Equation 2: (15m + 24b) × 5 = W
where m represents the work efficiency of a man and b represents the work efficiency of a boy.
We can simplify these equations by dividing both sides by 6 and 5 respectively:
Equation 1: 14m + 18b = W/6
Equation 2: 15m + 24b = W/5
Now, we can solve for m and b by using elimination or substitution. Once we have found the values of m and b, we can use them to solve for the time it would take 10 men and 12 boys to complete the work.
We can simplify the third equation using the values of m and b obtained from the first two equations:
(10m + 12b) × t = W
10m + 12b = W/t
where t represents the time, it takes for 10 men and 12 boys to complete the work.
Substituting the values of m and b from the first two equations into the third equation, we get:
(10×(W/324) + 12×(W/432)) × t = W
Simplifying and solving for t, we get:
t = 10.8 days
Therefore, it would take 10 men and 12 boys 10.8 days to complete the work.
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