If 6men can do a piece of work in 20 days and one man can do a work of 2 boys.Find how many days can 10 men and 5 boys do the same work ?
the work takes 120 man-days
10 men and 5 boys is like 12.5 men
120 / 12.5 = ?
man-days = 6(20) = 120
rate of man = 1/120 , where 1 represents the work done
rate of boy = 1/240
x(10)(1/120) + x(5)(1/240) = 1 , where 1 represents the work
x/12 + x/48 = 1
x(1/12 + 1/48) = 1
(5/48)x = 1
x = 48/5 = 9.6 days
or
since 1 boy does the job of 1/2 man, 5 boys ---> 2.5 men
so we have 10 men + 5 boys = 12.5 men
if 6 men can do the job in 20 days ---> 120 man-days
12.5 men can do it in 120/12.5 or 9.6 days
To solve this problem, we need to calculate the number of days it would take for 10 men and 5 boys to complete the work.
First, let's calculate the efficiency of work for each person. We are given that 6 men can complete the work in 20 days, so the efficiency of one man is 1/20 of the total work per day.
Next, we are given that one man can do the work of 2 boys. Therefore, one boy's efficiency is half of one man's efficiency, which is 1/(2*20) of the total work per day.
To find the efficiency of 10 men and 5 boys working together, we can add up their individual efficiencies. The efficiency of 10 men would be 10 times the efficiency of one man, and the efficiency of 5 boys would be 5 times the efficiency of one boy:
Efficiency of 10 men = 10 * (1/20)
Efficiency of 5 boys = 5 * (1/(2*20))
Now, to find how many days it would take for 10 men and 5 boys to complete the work, we need to divide the total work by their combined efficiency:
Number of days = Total work / (Efficiency of 10 men + Efficiency of 5 boys)
Since the total work for any given task is usually assumed to be one unit, we can simplify the equation:
Number of days = 1 / (Efficiency of 10 men + Efficiency of 5 boys)
Now, let's substitute the values we calculated earlier into the equation:
Number of days = 1 / (10/20 + 5/(2*20))
Number of days = 1 / (1/2 + 1/8)
To simplify further, we need to find a common denominator:
Number of days = 1 / (4/8 + 1/8)
Number of days = 1 / (5/8)
Now, to divide by a fraction, we can multiply by the reciprocal:
Number of days = 1 * (8/5)
Number of days = 8/5
So, it would take 8/5 (or 1.6) days for 10 men and 5 boys to complete the same work.