Question

SURESH STARTED HIS JOURNEY FROM P TO Q BY HIS BIKE AT THE SPEED OD 40 KM/HR AND THEN , THE SAME DISTANCE HE TRAVELLED ON HIS FOOT AT THE SPEED OF 10 KM /HR FROM Q TO R. THEN HE RETURNED FROM R TO P VIA Q AT THE SPEED OF 24 KM/ HR ..the average spped of the whole is.

A)18.5KM/HR
B) 19.8
C) 18.2
D)19.2

Answer 1

Let us consider the distance covered from P to R is 'd'
Hence total distance covered i.e from P to R and from R to P is '2d'
total time taken=(d/24)+(d/2)/40+(d/2)/10
since distance between P to Q is (d/2) and distance between Q to R is (d/2)
Hence total time taken=5d/48
Avg speed=total distance/total time
Avg speed=(2d)/(5d/48)
Avg speed=96/5=19.2km/hr

Answer 2

Solution :-

Let the distance from P to Q be 'x' km and from Q to R be 
'x' km also (as the distance from P to Q and from Q to R is same)

So, the distance from R to P via Q will be 2x.

Time taken from P to Q (t1) = x/40 hr

Time taken from Q to R (t2) = x/10 hr

Time taken from R to P via Q (t3) = 2x/24 hr

Total distance = 4x km

Total time taken = x/40 + x/10 + 2x/24

Taking LCM of the denominators and then solving it.

⇒ (3x + 12x + 10x)/120

⇒ 25x/120

⇒ 5x/24

Time taken is 5x/24 hrs

Speed = Distance/Time

⇒ 4x ÷ 5x/24

⇒ 4x*24/5x

⇒ 96x/5x

⇒ 96/5

⇒ 19.2 km/hr

So, the average speed is 19.2 km/hr.

So, the option (D) is correct.