1.
A man walks to a railway station at 3
 1 3
km/hr to catch 10 o�clock train but misses it by
3 minutes, the next day he walks at 3
 1 2
km/hr to catch the same train but misses it again
by 1 minute. Find the distance to the station.
• A.
2 km
•  C. 2 1 km 2
•  B. 2 1 km 3
•  D. 2 1 km 4
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Explanation :
Let the distance to the station be x km.
Given,
 x 10/3
-
 3 60
=
 x 7/2
-
 1 60

 3x 10
-
 2x 7
=
 3 60
-
 1 20
=>
 21x - 20x 70
=
 2 60

x =
 2 x 70 60
=
 7 3
km = 2
 1 3
km
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2.
A person covers the distance from P to Q at the speed of 3 km/hr. From Q to P he covers the distance at 6 km/hr. What is the average speed per hour?
• A.
3.5 km/hr
• C.
5 km/hr
• B.
4.5 km/hr
• D.
4 km/hr
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Explanation :
Average speed =
 2xy x + y
=
 2 x 3 x 6 3 + 6
=
 36 9
= 4km/hr
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3.
A man has to reach a place 40 km away. He walks at the rate of 4 km/hr for the first 16 km and then travels in a cart for the rest of the journey. Had he teavelled by cart for the first 16 km and covered the remaining distance on foot at 4 km/hr he would have taken an hour longer to complete the journey. Find the speed of the cart.
• A.
10 km/hr
• C.
6 km/hr
• B.
12 km/hr
• D.
8 km/hr
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Explanation :
Let the speed of the cart be x km/hr
Then duration of journey in the first case =
 16 4
+
 24 x

Duration of journey in the second case =
 16 x
+
 24 4

Given,
 16 4
+
 24 x
=
 16 x
+
 24 4
- 1
 24 x
-
 16 x
= 1 =>
 8 x
= 1 => x = 8
Speed of cart = 8 km/hr
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4.
A man standing on a 170 m long platform watches that a train takes 71/2 seconds to pass him and 21 seconds to cross the platform. Find the length of the train and its speed.
•  A. 94 4 m, 12 16 m/sec 9 27
•  C. 93 2 m, 11 12 m/sec 9 13
•  B. 94 4 m, 12 m/sec 9
• D.
96 m, 14 m/sec
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Explanation :

Ratio of speeds = 4 : 3 : 5

Ratio of times taken =
 1 4
:
 1 3
:
 1 5
=  15 : 20 : 12

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5.
A motorist covers the distance of 60 km from A to B at a speed of 20 km/hr and return journey from B to A at a speed of 30 km/hr. His average speed of entire journey is
• A.
22 km/hr
• C.
26 km/hr
• B.
24 km/hr
• D.
25 km/hr
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