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Quantitative Aptitude- Solve this Time, Speed and Distance Problem!

speed time distance problem

PSA_LEVEL-UP_QNR32. Shivaji and Ramna start on their motorbikes from Lucknow and Varanasi respectively to reach the other city. While Shivaji is riding at a speed of 25 km/h and Ramna is riding faster by 40%. If both the cities are 240 km apart,

i) when will they meet?

a) 3 hrs later
b) 4 hrs later
c) 2 hrs later
d) 5 hrs later

ii) how far is the meeting point from Lucknow?
a) 140 km
b) 120 km
c) 110 km
d) 100 km

iii) after meeting if both continue to ride towards the other city, how much more time do Shivaji and Ramna approx. take to reach their respective destinations?
a) 1.2 hrs; 2 hrs
b) 1.3 hrs; 2 hrs
c) 1.6 hrs; 2.58 hrs
d) 1.6 hrs; 2.85 hrs

Ans:

(i)
Shivaji’s speed = 25km/h
Ramna’s speed = 25*1.4 = 35km/h

Since, both of them are travelling towards each other, relative speed = 25km/h + 35km/h = 60 km/h
Time of meeting = Distance/Relative speed = 240/60 = 4 hrs. Option b.

(ii)

Since, time taken by both to reach the meeting point is same, distance is directly proportional to the speed.

Distance covered by Shivaji:Distance covered by Ramna = Speed of Shivaji: Speed of Ramna
= 25: 35
=5:7

Thus, distance between Lucknow and the meeting point = [5/(5+7)] * 240 = 100 km.

This distance can also be calculated as speed of Shivaji multiplied by 4 hrs (in which they meet each other)
= 25 km/hr * 4 hrs
=100 km. Option d.

(iii)

At meeting point, Shivaji has already covered 100 km and has to travel another 140 km.

He will take 140/25 hrs or 1.6 hrs more.
Similarly, at meeting point, Ramna has already covered 140 km and has to travel another 100 km.

He will take 100/35 hrs or 2.8 hrs more. Option d.

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