Amar Akbar and Antony decide to have a 39 x 39 m race Antony completes the race 14 m ahead of Amar A...........

Explanation:

When Antony completes, Amar would have run (x – 14) m; Time taken is the same
Ratio of Amar’s speed : Antony’s speed = x - 14 /t₁ : x/t1 or x - 14/x ......(i)
When Akbar finishes, Amar would have run (x – 32) m; Antony would have run (x – 20) m; Time taken is the same
At this point, the ratio of Amar’s speed : Antony’s speed = x - 32 /t₂ : x - 20/t2 or x - 32 /x - 20 .......(ii)

Alternate & intutive Approach:
When Akbar finishes the race, Antony is 20m away from the finish line and Amar is 32m away
When Antony finishes the race, Amar is 14m away from the finish line
This implies that in the same time Antony and Amar covered 20m and 32-14 = 18m respectively...
So the speeds of Antony and Amar will be in the ratio 20 : 18 or 10 : 9
That means, Amar's speed 9/10^th of Antony's speed.