BENCHHMARK

1. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. Find the ratio of their speeds ?

Answer: 3 : 2

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

⇒ ( 27x + 17y ) / ( x + y ) = 23

27x + 17y = 23x + 23y

27x – 23x = 23y – 17y

4x = 6y

( x / y ) = ( 6 / 4 )

( x / y ) = ( 3 / 2 )

x : y = 3 : 2

2. The distance between Jay′s and Mani′s places is 120 km. Jay travelled the whole distance from her place to Mani′s at 30 km/hr but returned at 40 km/hr. Her average speed for the whole journey is (approximately) ?

Answer: 34 km/hr

Explanation:

Average speed = ( 2 * x * y ) / ( x + y )

= ( 2 * 30 * 40 ) / ( 30 + 40 )

= ( 2 * 30 * 40 ) / 70

= 240 / 7

= 34.28 km/hr

Average speed for the whole journey ( approximately ) = 34 km/hr

3. A train is moving at a speed of 132 km/r. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long?

Answer: ( 7 * ( 1 / 2 )) sec

Explanation:

Speed of train = ( 132 * ( 5 / 18 )) m/sec

= ( 110 / 3 ) m/sec

Distance covered in passing the platform = ( 110 + 165 ) m

= 275 m

Time taken = Distance / Speed

= ( 275 / ( 110 / 3 )) sec

= ( 275 * ( 3 / 110 )) sec

= ( 15 / 2 ) sec

= ( 7 * ( 1 / 2 )) sec

4. How many minutes Raman will take to cover a distance of 400 meters if he runs at a speed of 20 km/hr ?

Answer: ( 1 * ( 1 / 5 )) mins

Explanation:

Raman′s speed = 20 km/hr

= 20 * ( 5 / 18 )

= ( 50 / 9 ) m/sec

Time = Distance / Speed

= 400 / ( 50 / 9 )

= 400 * ( 9 / 50 )

= 8 * 9

= 72 sec

= ( 1 * ( 1 / 5 )) mins