Tips on Solving Problems Based on Races & Games

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3 TIPS on cracking Aptitude Questions on Races
and Games
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Tip 1 Acquaint yourself with the terms
Dead Heat Race A race in which all the
contestants reach the Goal at the same
time. Start If A and B are two contestants in a
race, such that before the start of the race, A
is at the starting point and B is ahead of A by
12 meters, then we say that A gives B a start of
12 meters. Game A game of 100, means that the
person among the contestants who scores 100
points first is the winner. If A scores 100
points while B scores only 80 points, then we say
that 'A can give B 20 points. This implies that
if A actually gave B a start of 20 points, then
the contest would result in a dead heat.
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Tip 2 Assume that the speed or the scoring rate
for each player is constant
Question In a game of 100 points, A can give B
20 points and C 28 points. How many points can B
give C? Solution By the time A scores 100
points, B scores only 80 and C scores only 72
points. Let the Scoring Rate of A be Sa.
(Scoring Rate score/ time) Scoring Rate of B,
Sb 80/100 x Sa 0.8 Sa Scoring Rate of C, Sc
72/100 x Sa 0.72 Sa Time taken for B to get 100
points 100/Sb 100/ (0.8 x Sa) Score taken by
C in this time period Sc x 100/ (0.8 x Sa)
72/0.8 90 Thus, B can give C 10
points. Question In a 200 m race A beats B by
35 m or 7 sec. Find A's time over the
course. Solution By the time A completes the
race, B is 35m behind A and would take 7 more
seconds to complete the race. gt B can run 35 m
in 7 s. Thus, Bs speed 35 / 7 5 m/s. Time
taken by B to finish the race 200 / 5 40
s. Thus, As time over the course (40 7)s
33 s.
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Tip 3 If A runs x times faster than B, As
speed is actually 1x the speed of B.

• Question A runs 1? times as fast as B. If A
  gives B a start of 80 m, how far must the winning
  post be so that A and B might reach it at the
  same time?
• Solution
• Speed of A, Sa 5/3 x Sb
• Let the distance of the course be d meters
• Time taken by A to cover distance d Time
  taken by B to cover distance d-80
• d/5/3 x Sb (d-80)/Sb
• 3d 5d 400
• 2d 640 gt d 200m
• Question A runs 1? times faster than B. If A
  gives B a start of 80 m, how far must the winning
  post be so that A and B might reach it at the
  same time?
• Solution
• Speed of A, Sa (1 5/3) x Sb 8/3 x Sb
• Let the distance of the course be d meters
• Time taken by A to cover distance d Time
  taken by B to cover distance d-80
• d/8/3 x Sb (d-80)/Sb
• 3d 8d 640
• 5d 640 gt d 128m

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