Question

A and B together can do a piece of work in 15 days. If A's one day's work is times 2/3 times
B's one day's work; in how many days can A and B do the work alone? ​

Answer 1

Answer

Let 

A’s one day work be x and B’s one day work be y.

Then according to the question,

  x=23y

⇒2x=3y

⇒2x−3y=0      … (i)

Also given, in 15 days: A and B together can do a piece of work

So, according to this condition we have

  x+y=151

⇒15(x+y)=1

⇒15x+15y=1      … (ii)

Multiplying equation (i) by 5, we get

10x–15y=0       ... (iii)

Subtracting equation (ii) from (iii), we get

25x=1

⇒x=251

On substituting the value of x in equation (i), we get

  2⋅251−3y=0

⇒252=3y

⇒y=752

Therefore, 

Man A will do the work in x1 days =(1/25)1=25 days  and 

Man B will do the work in