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1.
In a km race, A beats B by 28 metres or 7 seconds. Find A's time over the course.
Answer & Solution
Answer: c) 4 min. 3 sec.

Solution:   Clearly, B covers 28 m in 7 seconds.

B's time over the course = [(7/28) * 1000] sec. = 250 seconds .

A's time over the course = (250 - 7) sec = 243 sec. 4 min. 3 sec.
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2.
A runs 1   3/4 times as fast as B. If A gives B a start of 84 m, how far must the winning post be so that A and B might reach it at the same time?
Answer & Solution
Answer: b) 196 m

Solution:   Ratio of the rates of A dn B = 7/4 : 1 = 7 : 4.

So, in a race of 7m, A gains 3 m over B.

3 m are gained by A in a race of 7 m.

85 m are gained by A in a race of [(7/3) * 84] m = 196 m.

Winning post must be 196 m away from the starting point.
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3.
A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B?
Answer & Solution
Answer: b) 50 m

Solution:   Clearly, A beats B by 10 sec.

Distance covered by B in 10 sec. = [(1000/200) * 10] m = 50 m .

A beats B by 50 metres.
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4.
In a 100 m race, A runs at 8 km per hour. If A gives B a start of 4 m and still beats him, by 15 seconds, what is the speed of B?
Answer & Solution
Answer: c) 5.767 km/hr

Solution:   Time taken by A to cover 100 m = [{(60 * 60) / 8000} * 100] sec. = 45 sec.

B covers (100 - 4) m = 96 m in (45 + 15) sec. = 60 sec.

B's speed = [(96 * 60 * 60) / (60 * 1000)] = km/hr = 5.76 km/hr.
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5.
A, B, and C are three contestants in a km race. If A can give B a start of 40 m and A can give C a start of 64 m, how many metre's start can B give C?
Answer & Solution
Answer: d) 25 m

Solution:   While A covers 1000 m, B covers (1000 - 40) m = 960 m and C covers (1000 - 64) m or 936 m.

When B covers 960 m , C covers 936 m.

When B covers 1000 m , C covers [(936/960) * 1000] m = 975 m.

B can give C a start of (1000 - 975) m or 25 m.
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6.
In a game of 80 points, A can give B 5 points and C 15 points. Then, how many points B can give C in a game of 60?
Answer & Solution
Answer: d) 8

Solution:   A : B = 80 : 75; A : C = 80 : 65

B/C = [(B/A) * (A/C)] = [(75/80) * (80/65)] = 15/13 = 60/52 = 60 : 52

In a game of 60, B can give C 8 points.
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7.
In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race, A beats B by:
Answer & Solution
Answer: c)20 m

Solution:   Distance covered by B in 9 sec. = [(100/45) * 9] m = 20 m .

A beats B by 20 metres.
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