The speeds of two bodies are in the ratio 2 : 3. If the difference in the time taken to cover 50 m is 10 sec, then find the difference in their speeds.

$\frac{5}{6}$m/sec

Let the speed of two bodies be 2S and 3S respectively.

 Time taken by first body to cover 50 m = \(\frac{50}{2x}\)

 Time taken by second body to cover 50 m = \(\frac{50}{3x}\)
 
 According to the question,

\(\frac{50}{2x}\) - \(\frac{50}{2x}\) = 10

50 = 10 × 6 x

x = \(\frac{50}{60}\)

= \(\frac{5}{6}\) 

Difference in speed = 3x - 2x = x

= \(\frac{5}{6}\)  m/sec