Question

4 men and 6 boys are finish the plece of 5 day while 3 men and 4 boy finish in 7 days. find finish take time 1 men alone and 1 boy alone

Answer 1

3let 1 man alone finish the work in x days and one boy finish the work in y days
then one man ,s one day ,s work =1/x
and 1boys one day work=1/y
4men and6 boys finish work in 5days
4 mens one day work +6 boys 1 day work=1/5
4/x+6/y= 1/5
LET 1/x=u and 1/y=v
4u+6v=1/5 equation 1
again 3 men and 4 boys finish work in 7 days
3mens 1 days work +4 boys one day work =1/7
3/x+4/y=1/73
let 1/x=u and 1/y=v
3u+4v=1/7 equation two
on multiplying equation one by 4and equation two by 6
we get
now
on subtracting
16u+24v=4/5
-18u+24v=6/7
-2u=-2/35
u=-2/35×-2
u=1/35
1/u=35
putting u=1/35
in equation two we get
3u +4v=1/7
3×1/35+4V=1/7
3/35+4V=1/2
4v=1/7-3/35
4v=5-3/2
v=2/35×4
v=1/70
now
u=1/x=1/35
x=35
now v=1/y=1/70
v=70
one man can finish alone the work in 35 days
and one boy can finish alone that work in 70 days