Question

2 men and 3 boys can do a piece of workin 10 days while 3 men and 2 boys can do thesame work in 8 days. in how many days can 2men and 1 boy do the work ?

Answer 1

there is two  answer  1

1 ans)

Let one man do the work alone in mm days. 
Let one boy do the work alone in bb days.

In one day 1m1m part of the work is done by 1 man and 
in one day 1b1b part of the work is done by 1 boy.
 
Now by given condition we have 
2×1m+3×1b=110  ⋯(A)2×1m+3×1b=110  ⋯(A)
(work done by 2 men and 3 boys in one day) 

We also have 
3×1m+2×1b=18  ⋯(B)3×1m+2×1b=18  ⋯(B) 

Solving above two equations we get 
1b=11001b=1100 and 1m=72001m=7200
 
We are asked to find how many days will 22 men and 11 boy take. 
First we find out work completed in one day by 22 men and 11 boy 
=2×7200+1100=8100=112.5=2×7200+1100=8100=112.5
 
Thus the work will be completed in 12.512.5 days

2 ans)

Let work done by 1 men on 1 day be m, one boy in 1 day be b

Work done by 2 men and 3 boys in 1 day = 110110
=> 2m + 3b = 110110 .............(1)

3 men and 2 boys can do the same piece of work in 8 days
Work done by 3 men and 2 boys in 1 day = 1818
=> 3m + 2b = 1818  .............(2)

Solve (1) and (2) to get values of m and b

(1)×3=> 6m +9b = 310310  .............(3)
(2)×2=> 6m +4b = 1414    .............(4)
(3)-(4)=> 5b = 120120
=> b = 11001100 

Using this value of b in (1)
2m + 3×1100=1103×1100=110 

2m +  3100=1103100=110 

2m = 71007100 

m = 72007200 


Work done by 2 men and 1 boy in 1 day = 2m + b 
=2×7200+1100=2×7200+1100 

=8100=225=8100=225 

Therefore, required number of days to complete the work if 2 men and 1 boy work
=252=1212