Question

8 men and twelve boys can finish a piece of work in 5 days while 6 men and 8 boys can finish it in 7 days find the time taken by one man alone and that by one boy alone to finish the waork.

Answer 1

Let the men's rate of work in jobs/man/day= a
Let the boys' rate of work in jobs/boy/day= b
Given:
8 men and 12 boys finish in 10 days
6 men and 8 boys finish in 14 days

so, we can also write
a*8*10 + b*12*10 = 1[job]
a*6*14 + b*8*14 = 1[job]
A.T.P(according to the problem)
80a + 120b = 1
84a + 112b = 1
#a + 3b/2 = 1/80
-> a = 1/80 - 3b/2
#3a + 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 = a = 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