8 men and 12 boys can finish a piece of work in 10 days. while 6 men and 8 boys can finish it in 14 days. find the time taken by 1 men alone and by 1 boy alone to finish the work.
Answers
Answer:
I think that with 1 man alone and 1 boy alone will finish the work in 98 days.
Answer:
one man can finish work in 140 days
Step-by-step explanation:
let the time taken by one man to complete the wrok be x and time taken by one boy to complete the work be y
so, in one day one man can complete 1/x part of the work and one boy can complete 1/y part of the work
since 8 men and 10 boys can finish a piece of work in 10 days
⇒8/x + 12/y = 1/10 and 6/x + 8/y = 1/14
since the eqaution are not linear , let 1/x = a and 1/y = b
⇒8a + 12b = 1/10 and 6a + 8b = 1/14
multiply the first equation by 3 and second equation by 4 , we get
24a + 36b = 3/10 and 24a +32b = 2/7
subract the equation obtained
24a + 36b - 24a - 32b = 3/10 - 2/7
4b= 1/70 ⇒ b = 1/280
substitute in the equaton 8a + 12b = 1/10 to obtan the value of a
8a + 12(1/280) = 1/10 ⇒ a = 1/140
so, x = 1/a ⇒ 140 and y = 1/b = 280
hence one man can finish work in 140 days