Question

8 men and 12 boys can finish a work in 10 days while 6 men and 8 boys can finish it in 14 days. find the time take by 1 man and 1 boy alone to finish the work ​

Answer 1

Given:-

8men +12 boys=work in 10days

6men + 8boys=work in 14 days

Find:-

Time taken by a boy and man to finish the work

Solution:-

Let, a boy can do the job =Bdays

a man can do the job=Mdays

Solve the problem by equation process

=>8M+12B=1/10-------(1)

=>6M+8B=1/14---------(2)

In eq 1st multiplying by 6 and in eq 2nd multiplying by 8 here]

=>48M+72B=6/10

=>48M+64B=8/14

By solving equation we get,

=>8B=6/10-8/14

=>8B=42-40/70

=>8B=2/70

=>4B=1/70

=>B=1/280

Now, putting the value of B in eq 1st

8M+12B=1/10

=>8M+12(1/280)=1/10

=>8M+3/70=1/10

=>8M=1/10-3/70

=>8M=7-3/70

=>8M=4/70

=>2M=1/70

=>M=1/140

Hence,

=>A man take 140 days to finish the work

=>A boy take 280 days to finish the work