Below are three simple problems based on relative speeds. Though the calculations are simple, the questions are in the form of 'short stories' with lot of text. You have to practice to quickly glance through these types of questions and extract only relevant data necessary to solve.

Question 1

Akilan and Ramesh Raman are good friends. On a Friday, they went to a restaurant near their college. After the dinner, both of them hired a bicycle each and left to their places in opposite directions. Akilan started cycling towards north at 10 kmph and Ramesh Raman started cycling at 8 kmph towards south. It was 8 pm when they started. If their residences are 45 kms apart, by what time both would have reached their homes?

(a) 10.00 PM (b) 10.30PM (c)11.00PM (d)11.30 PM

Answer : b) 10.30PM

Solution:

Relative speed of Akilan with respect to Ramesh Raman = 10 + 8 = 18 kmph (we are adding speeds as they are travelling in opposite directions).

Maximum time by which both the friends would have reached their homes = Distance between the homes / Relative speed = 45/18 = 2.5 hours.

(Note : We would have got the same answer even if we had started by calculating relative speed of Ramesh Raman with respect to Akilan.)

2.5 hours from 8pm is 10.30pm which is our answer.

Question 2

The great Chinese mathematician, Lee Quan used to write fantastic stories in which he embedded a number of brain teasers and curious puzzles.In one of his famous books, he created a character Tory. Tory travels to dream worlds and meets strange persons like Green King and Mare Harch.After conversing with Tory in their dreams both Green King and Mare Harch started moving in clouds towards each other. Green King moved at a speed of 1200 kmph and Mare moved at a speed of 1800 kmph. The initial distance between them was 6000 Km. After flying they met each other exactly at 2.00 AM. Can you guess the time when they last conversed with Tory ?

(a) 3.00AM (b) 10. 00 PM (c) 12.00AM (d) 1.00 AM

Answer : c) 12.00AM

Solution:

Relative speed of Green King with respect to Mare Harch = 1200 + 1800 = 3000 kmph (we are adding as their flying directions are opposite to each other)

Distance between the two = 6000 km

Time taken for them to meet = Distance / Relative Speed = 6000/3000 = 2 hours.

They had started after conversing with Tory. Therefore, calculating the time of their start will give the time they last conversed with Tory.

Time of their start = 2 hours before 2.00 AM which is 12 AM.

Question 3

Roshan and Kishan are good friends. Roshan purchased a second hand Ferrari free of duty for Rs 84 lakhs. Kishan can drive his Mercedes at an average speed of 44 km per hour while Roshan was able to drive Ferari 3 times faster than Kishan. After a nice garden dinner in a Full Moon day they moved in opposite directions with the above stated speeds. When will both Roshan and Kishan would be 880 kilo meters apart from each other?

(a)4 hrs after (b)4 ½ hours after (c) 5 hours after (d) 5 ½ hours after

Answer : c) 5 hours after

Solution:

Kishan’s speed is 44 kmph and Roshan’s speed = 3x44 =132 kmph

Relative speed of Kishan with respect to Roshan = 44+132 =176 kmph. They had to cover a distance of 880 km in opposite directions.

So, Time to cover 880km = Distance / Relative Speed = 880 / 176 = 5 hours.

They would be 880 km apart after 5 hours.