Question

8 men and 12th boys can complete a piece of work in 10 days while 6 men and 8 boys can complete it in 14 days find the time taken by one man alone and that of one boy alone to finish the work suppose that one man can finish the work in 6 days and 1 boy can finish the work in y days then​

Answer 1

Step-by-step explanation:

Suppose that one man alone can finish the work in x days and one boy alone can finish it in y days. Then,

One man's one day's work =

x

1

One boy's one day's work =

y

1

∴ Eight men's one day's work =

x

8

12 boy's one day's work =

y

12

Since 8 men and 12 boys can finish the work in 10 days

10(

x

8

+

y

12

)=1⇒

x

80

+

y

120

=1 ..(i)

Again, 6 men and 8 boys can finish the work in 14 days.

∴14(

x

6

+

y

8

)=1⇒

x

84

+

y

112

=1 (ii)

Putting

x

1

=u and

y

1

=v in equations (i) and (ii), we get

80u+120v−1=0

84u+112v−1=0

By using cross-multiplication method, we have

−120+112

u

=

−80+84

−v

=

80×112−120×84

1

⇒

−8

u

=

−4

v

=

−1120

1

⇒u=

−1120

−8

=

140

1

and v=

−1120

−4

=

280

1

Now, u=

140

1

⇒

x

1

=

140

1

⇒x=140

and, v=

280

1

⇒

y

1

=

280

1

⇒y=280.

Thus, one man alone can finish the work in 140 days and one boy alone can finish the work in 280 days.