Question
Download Solution PDFWhile travelling from A to B, Raghav travels a quarter of the distance at 10 km/h, the next quarter of the distance at 15 km/h, the third quarter of the distance at 20 km/h, and the final quarter of the distance at 30 km/h. While travelling on exactly the same route, Manish travels for a quarter of the total time taken for his journey at 10 km/h, the next quarter of the total time taken for his journey at 15 km/h, the third quarter of the total time taken for his journey at 20 km/h, and the final quarter of the total time taken for his journey at 30 km/h. If the overall average speed of Raghav during his journey is given as y km/h, and that of Manish is given as z km/h, find the value of (z – y).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Raghav travels a quarter of the distance at 10 km/h, next quarter at 15 km/h, third quarter at 20 km/h, and final quarter at 30 km/h.
Manish travels a quarter of the total time at 10 km/h, next quarter at 15 km/h, third quarter at 20 km/h, and final quarter at 30 km/h.
Overall average speed of Raghav = y km/h
Overall average speed of Manish = z km/h
Formula used:
Average speed = Total distance / Total time
Calculations:
Let total distance = D
For Raghav:
Time taken for each quarter distance:
Time1 = D/4 × (1/10) = D/40
Time2 = D/4 × (1/15) = D/60
Time3 = D/4 × (1/20) = D/80
Time4 = D/4 × (1/30) = D/120
Total time for Raghav:
Total timeR = D/40 + D/60 + D/80 + D/120
⇒ Total timeR = D(1/40 + 1/60 + 1/80 + 1/120)
⇒ Total timeR = D(6 + 4 + 3 + 2) / 240
⇒ Total timeR = D(15/240)
⇒ Total timeR = D/16
Average speed of Raghav (y):
y = D / (D/16) = 16 km/h
For Manish:
Let total time = T
Distance covered in each quarter time:
Distance1 = T/4 × 10 = 10T/4
Distance2 = T/4 × 15 = 15T/4
Distance3 = T/4 × 20 = 20T/4
Distance4 = T/4 × 30 = 30T/4
Total distance for Manish:
Total distanceM = 10T/4 + 15T/4 + 20T/4 + 30T/4
⇒ Total distanceM = (10 + 15 + 20 + 30)T / 4
⇒ Total distanceM = 75T / 4
Average speed of Manish (z):
z = Total distance / Total time
z = (75T/4) / T
⇒ z = 75/4
⇒ z = 18.75 km/h
Value of (z - y):
z - y = 18.75 - 16
⇒ z - y = 2.75
∴ The correct answer is option 2.
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