If 3/x+y+2/x−y=2 and 9/x+y−4/x−y=1, then what is the value of x/y?

 

Correct Answer: 5

 

Given, 3/x+y+2/x−y=2 …(i)

 

and 9/x+y−4/x−y=1 …(ii)

 

Let x + y = a and x – y = b

 

On multiplying Eq. (i) by 3 and subtracting from Eq. (ii), we get

 

9/a−4/b=1

 

9/a+6/b=6

 

−10/b=5

 

Therefore, b = 2

 

Now, on putting the value of b in Eq. (i), we get

 

3/a+2/2=2

 

3/a=2−1

 

= a = 3 = x+y = 3 …(iii)

 

and x-y = 2 …(iv)

 

On subtracting Eq. (iv) from Eq. (iii), we get

 

2y = 1

 

Therefore, y=1/2

 

Now, putting y=12 in Eq. (iii), we get

 

x+1/2=3

 

= x = 3−1/2=6−1/2=5/2

 

Therefore, xy=5/2/1/2=5/2×2/1=5