Dear Reader, Below are three moderately difficult distance time problems to practice for Syntel papers.
Question 1
Brindavan Express started from Chennai Central Station at 7.10 am. Karnatak express train for the same destination started from the same station on the same day at 8.40 am and ran with an average speed of 60 km/hour. Karnatak express crossed the Brindavan Express at 11.40 am. Find the average speed of Brindavan Express.
a) 75 km/hr b) 40 km/hr c) 30 km/hr d) 45 km/hr
Answer : b) 40 km/hr.
Solution :
Karnatak Express train crosses the Brindavan Express in three hours
Distance covered by Karnatak express when it crosses Brindavan Express = Speed of Karnatak Express x Time Until It Crosses Brindavan = 60 x 3 = 180 km
This means that, Brindavan express would had covered the same distance 180 Km from Chennai when it is crossed (Overtook) by Karnatak.
The distance covered by Brindavan Express from 7.10 am till 11.40 am = 180 km (in 4 1/2 hours)
So the average speed of Brindavan Express is = Distance covered by Brindavan till crossing / Time taken till crossing = 180 / 4 1/2
180 / 9 x 2 = 40 km/hour
Question 2
A Tata Indica car started from Mumbai towards Kolkata at 6 am and travelled at an average speed of 60 km/hr. It was found that an important material to be sent to Kolkata was omitted to be included in the packets sent in Tata Indica car. The omitted material was carried on an Innova car that started at 8.15 am and travelled with an average speed of 90 km/hr. At what time Innova car will cross Tata Indica car ?
a) 1.15 pm b) 3.15 PM c) 12.45 pm d) 4.15 pm
Answer : c) 12 . 45 p.m.
Solution :
Indica had started 2 hours 15 mins in advance to that of Innova Car
Before, Innova started, Tata Indica covers a distance of 135 km in 2 hours and 15 minutes. (you can check this by using the formula Speed x Time where speed of Indica = 60km)
Innova travels at 90 km/hr.
Relative speed of Innova with respect to Indica = Speed of Innova - Speed of Indica = 90 - 60 = 30 km/hr
Time that would be taken by Innova to catch up with Indica = Distance Difference at Start of Innova/ Relative Speed of Innova with respect to Indica = 135/30 = 4 1/2 hours for Innova to cross Tata Indica
Innova started at 8.15 am . It will cross Tata Indica at 12.45 pm.
Question 3
A Transport bus started Madurai Bus Terminal at 7 am and travelled at an average speed of 40 km per hour till 8.30 am. This bus stopped at the on-way hotel for breakfast till 9 am and travelled at an average speed of 30 km per hour thereafter till its destination. Another express bus started from Madurai at 11 am and travelled at an average speed of X km per hour. The Express bus crossed the transport bus at 5 pm on the same day. Find the value of X?
a) 60 km/hr b) 40 km/hr c) 20 km/hr d) 50 km/hr
Answer : d) 50 km/hr
Solution :
Transport bus travelled at average speed of 40 km/hour
For 1 1/2 hours (i.e from 7 am till 8.20 am) Distance covered = 60 km.
Express bus starts at 11 am.
Till the express bus starts, transport bus would have covered further distance of
30 x 2 = 60 km.
Total distance covered upto 11 am by Transport bus is 60 + 60 = 120 km
Transport bus is travelling further at an average speed of 30 km per hour.
Express bus crossed Transport bus at 5 pm after travelling for 6 hours
Distance covered by the Transport bus till 5 pm = 120 + 180 = 300 km
This distance of 300 km is covered by express bus in 6 hours.
Hence average speed of Express bus = X = 300/6 = 50 km/hour