Overlapping Set Problem

Let x be the number of red balls in the jar and y be the number of green balls in the jar.

Then we know that n(red U green) = number of total balls in the jar = 87 (as it is given that each ball has at least one of two colors)

=> 87 = x + y - (3/7)*y [because 3/7 of the balls that have green color also have red color]
Also (2/7) * x = (3/7) * y [because 2/7 of the balls that have red color also have green color and it is given that 3/7 of the balls that have green color also have red color. These two numbers have to be equal].

Solving these two equations, we get y = 42 and x = 63.

So there are 63 red balls and 42 green balls in the jar.

Of these, number of only red balls = 63 - (2/7)*63 = 45
Number of only green balls = 42 - (3/7) * 42 = 24
Number of balls that are both green and red = 87 - 45 - 24 = 18

Therefore fraction of balls in the jar that have both red and green colors = 18/87 = 6/29

The correct answer is therefore (D).