Question

8 men and 12 boys complete work in 10 days and 6 men 8boys can finish the work in 14 days find time taken to finish work by one men alone

Answer 1

Let m = the men's rate of work in jobs/man/day
Let b = the boys' rate of work in jobs/boy/day
Given:
8 men and 12 boys finish in 10 days
6 men and 8 boys finish in 14 days
For these two jobs, we can write
m*8*10 + b*12*10 = 1[job]
m*6*14 + b*8*14 = 1[job]
80m + 120b = 1

84m + 112b = 1

m + 3b/2 = 1/80 -> m = 1/80 - 3b/2

3m + 4b = 1/28 -> 3(1/80 - 3b/2) + 4b = 1/28
Solve for b:
3/80 - 9b/2 + 4b = 1/28
b/2 = 3/80 - 1/28 = 21/560 - 20/560 = 1/560
b = 1/280 [jobs/boy/day]
If one boy is working alone, the rate is 1 job per 280 days, so it would take 280 days to finish
The men's rate = m = 1/80 - (3/2)(1/280) = 7/560 - 3/560 = 4/560 = 1/140
Thus a man working alone would need 140 days to complete the job