Question

A and B together finish a work in 4 days. If A alone can finish the work in 5 days, find in how many days will B alone finish the same work?

Its due in 3 minutes pls help

Answer 1

Answer:

Step-by-step explanation:

Let A's one day work be  

x

1

​  

 and B's one day work  

y

1

​  

.

It is given that A and B can complete work together in 5 days, therefore, we have:

A+B=  

x

1

​  

+  

y

1

​  

=  

5

1

​  

 

⇒  

xy

y

​  

+  

xy

x

​  

=  

5

1

​  

 

⇒  

xy

y+x

​  

=  

5

1

​  

 

⇒5(x+y)=xy.....(1)

A worked at twice his speed means  

x

2

​  

 

B worked at half of his speed means  

2y

1

​  

 

Together they complete work in 4 days, therefore, we have:

x

2

​  

+  

2y

1

​  

=  

4

1

​  

 

⇒  

2xy

4y

​  

+  

2xy

x

​  

=  

4

1

​  

 

⇒  

2xy

4y+x

​  

=  

4

1

​  

 

⇒4(x+4y)=2xy

⇒2(x+4y)=xy

⇒2x+8y=xy.....(2)

Substitute equation 2 in 1:

5x+5y=2x+8y

⇒5x−2x=8y−5y

⇒3x=3y

⇒x=y

x=y means that number of days worked by A alone is equal to B alone.

Now, substitute the value in equation 1:

x

1

​  

+  

x

1

​  

=  

5

1

​  

 

⇒  

x

1+1

​  

=  

5

1

​  

 

⇒  

x

2

​  

=  

5

1

​  

 

⇒x=5×2

⇒x=10

Hence, it would take 10 days for A alone to complete the job.