8men & 12 boys can finish a piece of work in 10days while 6 men and 8 boys finish it in 14 days find the time taken to complete the work by a man and a boy alone
Answers
Answer: 101.8181 days
Step-by-step explanation:
Step-by-step explanation:
8 men and 12 boys together can finish work in 10 days
thus 1 day work by them will be 1/10 part
⇒ 8m + 12b = 1/10 --------(1)
similarly 6 men and 8 boys together can finish work in 14 days
thus 1 day work by them will be 1/14 part
⇒ 6m + 8b = 1/14 ------(2)
now solving above two equations
multiply first by 6 and second by 8 we get
48m + 72b = 6/10
48m + 64b = 8/14
8b = 6/10 - 8/14
8m = 1/35
⇒ 1m = 1/280
now solving for b with the help of second equation
6/260 + 8b = 1/14
8b = 1/20
⇒ b = 1/160
thus one day work of one men = 1/280 part
and one day work of one boy = 1/160 part
hence one day work of one boy and one man = 1/280 + 1/160 = 44/4480 part
thus time taken to complete whole work will be = 4480/44 = 101.8181 days Ans.