Speed, Time and Distance Questions for CAT with Answers PDF

The monkey climbs 3 feet in 1 hour and drops by 2 feet in half an hour.
So, he climbs net 1 foot in (3/2) hours.
This way, he climbs 12 feet in 18 hours.
In the next hour, he will climb 3 more feet i.e. he will climb 15 feet in 19 hours and will reach the top of the tree.

Total distance = 1000 km
Total time = 16 hours
Let the time for bus travel be x hours.
Then, time for taxi travel be (16 – x) hours.
Then,
1000 = x × 80 + (16 – x)36
1000 = 80x + 576 – 36x
424 = 44x
x = 424/44 = 106/11 hours
Distance covered by bus = = 770.9 km

Given, race is to end in a dead heat i.e. they are all supposed to cross the finish line at the same time.
Position of x from finish line = 1000
Position of y from finish line = 1000 - 50 = 950
Position of z from finish line = 1000 - 69 = 931
So, y can give a 19 m start to z for the given scenario to be true.

Let L = Length of train
Speed =  ........ (1)
Speed = L/16 ........ (2)
From (1) and (2),
L/16 = 
⇒ L = 240 m
Speed = L/16 =  240/16 = 15 m/s =  = 54 kmph

Distance covered by A is L metres to finish the race.
Then, distance covered by B = L - x₁ metres
Distance covered by C = L - x₃ metres
C beats B, if and only if the distance covered by C at that moment is greater than B.
So, (L - x₃) > (L - x₁)
Solving, x₁ > x₃.

When the trains are travelling in opposite direction, the sum of their speeds (relative speed) = (227.5/3.25) = 70 kmph
If they had been travelling in same directions, the difference of their speeds (relative speed) = (32.5/3.25) = 10 kmph
Hence, the speed of the faster train = (70 + 10)/2 = 40 kmph and the speed of the slower train = (70 - 10)/2 = 30 kmph

Speed of Javed = 1 stair/min
After sixteen minutes, relative distance between Javed and Salma = 16 stairs
Speed of Salma = 2 stairs/min
Relative speed of Salma w.r.t. Javed = 2 - 1 = 1 stair/min
Time taken by Salma to cross Javed = 16/1 = 16 minutes

Let the length of Train A be 2L and the length of Train B be L.
Speed of Train A = 45 kmph = 12.5 m/s and speed of Train B = 22.5 m/s
According to the given condition,
4 = 
L =  m
Let length of tunnel be t.
So, 4 × 60 = 
Putting the value of L in the above equation and solving,
t = 2906.67 m = 2.9 km = 3 km (Approx.)

Assume length of platform = L metres
Speed of first train = V m/sec
According to the given condition,
50V = L + 500
Speed of second train = 500/20 = 25 m/sec
Therefore, speed of first train = 12.5 m/sec
Hence, length of platform = 50 × 12.5 - 500 = 625 - 500 = 125 m

 Total time he travelled = 5 hours 10 minutes (∵ Varun rested for 50 minutes.)
So, d = 60 × 5 = 60 × 31/6 = 310 km