If $$\frac{x-y}{3}=\frac{x+y}{5}=\frac{xy}{8}$$​, then find the value of xy.

Correct option is D

Given:

​$$\frac{x - y}{3} = \frac{x + y}{5} = \frac{xy}{8}$$​

Solution:

Let the common value be k, i.e.,

​$$x - y = 3k, \quad x + y = 5k, \quad xy = 8k$$​​

Add the first two equations:

(x - y) + (x + y) = 3k + 5k

2x = 8k => x = 4k

Subtract the first equation from the second:

(x + y) - (x - y) = 5k - 3k

​$$2y = 2k \Rightarrow y = k$$​

Substitute x = 4k and y = k into xy = 8k :

(4k)(k) = 8k

​$$4k^2 = 8k$$​

​$$4k^2 - 8k = 0$$​

4k(k - 2) = 0

k = 2 (since k = 0 is not valid)

xy = 8k = 8(2) = 16