Aptitude

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📘 Height-and-Distance
📘 series
📘 Time and Distance
📘 Time and Work
📘 Train

94. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

by
[A]. 100 kmph
[B]. 110 kmph
[C]. 120 kmph
[D]. 130 kmph
✅ The correct answer is option C.
Let speed of the car be x kmph.

Then, speed of the train =
150
x
=

3
x
kmph.

100
2

75
–
75
=
125

x
(3/2)x
10 x 60

75
–
50
=
5

x
x
24

x =

25 x24

= 120 kmph.

5

95. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

by
[A]. 70 km/hr
[B]. 75 km/hr
[C]. 84 km/hr
[D]. 87.5 km/hr
✅ The correct answer is option D.
Let the speed of two trains be 7x and 8x km/hr.

Then, 8x =

400

= 100

4

x =

100

= 12.5

8

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

97. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

by
[A]. 8 kmph
[B]. 11 kmph
[C]. 12 kmph
[D]. 14 kmph
✅ The correct answer is option C.
Let the distance travelled by x km.

Then,
x
–
x
= 2

10
15

3x – 2x = 60
x = 60 km.

Time taken to travel 60 km at 10 km/hr =

60
hrs
= 6 hrs.

10

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed =

60
kmph.
= 12 kmph.

5

98. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:

by
[A]. 300 kmph
[B]. 360 kmph
[C]. 600 kmph
[D]. 720 kmph
✅ The correct answer is option D.
Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr.     [We can write 1 hours as 5/3 hours]

Required speed =

1200 x
3
km/hr
= 720 km/hr.

5

99. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

by
[A]. 2 : 3
[B]. 3 : 2
[C]. 3 : 4
[D]. 4 : 3
✅ The correct answer is option C.
Let the speed of the train be x km/hr and that of the car be y km/hr.

Then,
120
+
480
= 8      
1
+
4
=
1
….(i)

x
y
x
y
15

And,
200
+
400
=
25
   
1
+
2
=
1
….(ii)

x
y
3
x
y
24

Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.