Question

.2 men and 5 boys 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 by one man alone to
finish the work and that taken by one boy alone to finish the work.​

Answer 1

Step-by-step explanation:

let the time taken by one man be=x

and by one boy be=y

then the equations formed will be

eq1: 2/x+5/y=1/4

eq2: 3/x+6/y=1/3

so by solving eq1

we get, eq3: 8x+20y=xy

and by solving eq2

we get, eq4: 9x+18y=xy

now, subtract eq3 by eq4

we get, x-2y=0

eq5:=》y=x/2

substitute eq5 in eq4

we get, 9x+9x=x × x/2

then,=》18x=x × x/2

=》18x×2=x × x

=》36x=x × x

=》36=x × x/x

eq6:36=x

now, substitute eq6 in eq4

we get, 324 + 18y=36y

now, 324=36y-18y

=》 324=18y

=》324/18=y

=》18=y

therefore the time taken by one man =36 days and that by one boy =18 days