Question

2. 5 men and 5 boys together can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. Find the time taken of one man alone to finish the work and that taken by one boy alone to finish the work.

Ans: 18 days , 36 days

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Answer 1

let 1 men can finish the work in x days and 1 boy can finish the work in y days.

then 1 man's 1 day work = 1/x and 1 boy's one day work = 1/y

according to the question---

2/x + 5/y = 1/4    ------ (1)

3/x + 6/y = 1/3    --------(2)

put 1/x =  u and 1/y = v in eq, (1) and (2)

2u + 5v = 1/4 

= 8u + 20 v = 1    ----------- (3)

3u+ 6v =1/3

= 9u + 18 v = 1     ------------(4)

solving equation  3 and 4

multiply equation 3 with 9 and 4 with 8

         9 (8u +20v =1)

        8( 9u + 18v =1)

 by multiplying we get

 72u + 180v =9         ------ (5)

 72u + 144v =8        -------(6)

now subtract eq. 5 from 6

        72u + 180v =9  

        72u + 144v =8    

       -          -          -

   _______________________

                   36V = 1  

      so v= 1/36 

put v = 1/36 in eq. 3

      8u + 20 X 1/36 = 1

   8u =4/9  

      72u = 4

     u = 1/18

u= 1/x = 1/18

       x = 18 days 

 v = 1/y = 1/36

      y = 36 days

 so man can finish work in 18 days and boy can finsh work in 36 days