If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
📊 Work and Time Calculation 📊
Let’s analyze the situation:
6 men + 8 boys = 1/10 of the work per day (10 days to complete)
26 men + 48 boys = 1/2 of the work per day (2 days to complete)
We can set up equations based on the work rates:
6m + 8b = 1/10
26m + 48b = 1/2
To simplify, multiply the first equation by 5:
30m + 40b = 1/2
Now, subtract this equation from the second equation:
(26m + 48b) – (30m + 40b) = 0
-4m + 8b = 0
Simplify:
m = 2b
Now, substitute m = 2b into one of the original equations:
6(2b) + 8b = 1/10
12b + 8b = 1/10
20b = 1/10
b = 1/200 (work done by 1 boy per day)
Now, find the work done by 1 man per day:
m = 2b
= 2/200
= 1/100 (work done by 1 man per day)
Now, calculate the work done by 15 men and 20 boys per day:
15 men = 15/100 = 3/20
20 boys = 20/200 = 1/10
Total work done per day = 3/20 + 1/10
= (3/20) + (2/20)
= 5/20
= 1/4
Time taken by 15 men and 20 boys = 1 / (1/4)
= 4 days
🎉 The time taken by 15 men and 20 boys will be 4 days. 📊
