 # CAT: Quantitative Ability - Distance & Speed Questions CAT Result Date: 21st December 2022  ### Question 1)

A 270 metres long train running at the speed of 120 Kmph crosses another train running in opposite direction at the speed of 80kmph in 9 seconds. What is the length of the other train?

A) 230 m

B) 240 m

C) 260 m

D) 320 m

E) None of the these

Solution:

Relative speed = (120 + 80) km/hr

= (200*5/18) m/sec = 500/9 m/sec

Let the length of the other train be X metres

Then, X+ 270/9 = 500/9

X = 230

### Question 2)

Two trains, each 100 m long, moving in opposite direction, cross each in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

A) 30Km/hr

B) 45Km/he

C) 60Km/hr

D) 75Km/hr

Solution:

Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2x m/sec.

Relative speed = (x + 2x) m/sec = 3x m/sec.

(100 + 100)/8 = 3x

24x = 200

X = 25/3

So. Speed of the faster train = 50/3 m/sec

= (50/3*18/5) Km/hr = 60Km/hr

### Question 3)

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 Km/hr respectively in opposite direction on parallel tracks. The time (in seconds) which they take to cross each other, is:

A) 9

B) 9.6

C) 10

D) 10.8

Solution:

Relative speed = (60 + 40) km/hr = (100*5/8) m/sec = 250/9 m/sec

Distance covered in crossing each other = (140 + 160) m = 300 m

Required time = (300*9/250) sec. = 10.8 sec

### Question 4)

A train 800 metres long is running at a speed of 78 Km/hr. If it cross a tunnel in 1 minute, then the length of the tunnel (in metres) is:

A) 130

B) 360

C) 500

C) 540

Solution:

Speed = (78*5/18) m/sec = (65/3) m/sec

Time = 1 minute = 60 seconds

Let the length of the tunnel be x metres.

Then, (800 + x/60) = 65/3

3(800 + x) = 3900

X = 500

CAT 2022 exam is being conducted in November 27, 2022

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