Question

4 Men 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in 7 days. find the time taken by one man alone and that by one boy alone to finish the work

Answer 1

Let time taken by a boy to complete work =x
and that of boy be y
so in 1 day work done
by man=1/x
by boy =1/y
ATQ
4/x+6/y=1/5
let 1/x =a and 1/y=b
so 4a+6b=1/5
20a+30b=1.......(1)

Now
3/x+4/y=7
3a+4b=7
21a+28b=1........(2)
Multiply eq1 by 21 and eq2 by 20
then by elimination method,

21(20a+31b= 1) .
 20(21a+28b =1)

420a -420a +630b - 560 b  =21-20

70 b= 1        b = 1/70 and y=70 days
putting it in eq1 we get x=35 days
 
1 man can do work in 35 days
1 boy can do work in 70 days