A and B start moving towards each other from places X and Y, respectively, at the same time. The speed of A is 20% more than that of B. After meeting on the way, A and B take $2\frac{1}{2}$ hours and x hours, now to reach Y and X, respectively. What is the value of x ?

$3\frac{3}{5}$

As , speed increased by 20%

Let initial speed = 5

Increased speed = 6

Time taken by B after meeting is =  x hours

Formula used :-

(\(\frac{Speed \;of\; A }{Speed \;of\; B}\))2 = \(\frac{Time \;of\; B }{Time \;of\; A}\)

(\(\frac{6 }{5}\))2 = \(\frac{x × 2 }{5}\)

(\(\frac{36 }{25}\)) = \(\frac{2x }{5}\)

x  = 3\(\frac{3}{5}\) hours