8men and 12boys can finish a piece of work in 10 days while 6 men and a voice can finish in 14 days find the time taken by one man alone and that one boy alarm to finish that work
Answers
Answer:
Step-by-step explanation:
Let one man alone can finish the work in x days and one boy alone can finish the work in y days.
In one day man can do
x
1
th work , then 8 man can do
x
8
th part of work.
In one day man can do
y
1
th work , then 8 man can do
y
12
th part of work.
Given together they can finish in 10 days
∴
x
8
+
y
12
=
10
1
Again 6 man can do in one day =
x
6
parts of the work.
Again 8 boy can do in one day =
y
8
parts of the work.
Given that together they can finish in 14 days.
∴
x
6
+
y
8
=
14
1
Putting
x
1
=u and
y
1
=v we get the following equations
8u+12v=
10
1
⇒80u+120v=1
And
6u+8v=
14
1
⇒84u+112v=1
By Cross multiplication, we get
⇒
120−112
u
=
84−80
v
=
8960−10080
−1
⇒
8
u
=
4
v
=
−1120
−1
⇒u=
−1120
−8
=
140
1
⇒v=
−1120
−4
=
280
1
Now u=
140
1
=
x
1
⇒x=140
Now v=
280
1
=
y
1
⇒y=280
Thus one man alone can finish work in 140 days and one boy alone can finish work in 280 days