The ratio of distance between two places A and B to the distance between places B and C is 3 : 5.  A man travels from A to B at a speed of x km/h and from B to C at a speed of 50 km/h.  If his average speed for the entire journey is 40 km/h, then what is the value of (x - 20) : (x + 2)?

5 : 16

Let, distance b/w A to B is 30 km and B to C is 50 km, so total is 80 km.

                    AB   :    BC      Total

Distance       3    :    5         8 Unit

Average speed = 40 km/h

Time = \(\frac{80}{40}\) = 2 hours

Total time = 2 hours (to travel A to C)

Here,

Speed to travel B to C = 50 km/hr and distance = 50 km

So, Time to travel B to C = \(\frac{50}{50}\) = 1 hour

Therefore, Time to travel from A to B = 2 - 1 = 1 hr.

⇒ Speed from A to B (x)= \(\frac{30}{1}\) = 30 km/h

⇒ x = 30

Now,

(x - 20)     :   (x + 2) 

(30 - 20 )  :  (30 + 2)

        10    :     32

⇒       5    :    16