## 3 Solved Races & Games Problems To Prepare For Accenture Aptitude Tests

Below are three problems based on Races and Games.

Points to know:

Games: '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'.

Question 1

In a game of 200m race, A can win B by 50 m and B can win C by 8 m. In the same race, A can win C by:

a) 52m b) 58m c) 56m d) 54m

Solution :

Given that, A can win B by 50 m.

That is, When A runs 200 m then B can run (200 - 50 = )150 m.

And, B can win C by 8 m means, When B runs 200 m then C can run (200 - 8 =) 192 m.

Therefore, A:B = 200:150 and B:C = 200:192

We have to find A : C.

A:C = A/C = A/B x B/C
= (200 / 150) x ( 200 / 192) = (4 / 3) x (200 / 192) = 200 / (3 x 48) = 200 /1 44

(Note that, we have to find the result in 200m race, so that, we have to keep 200 in numerator).

That is, A:C = 200:144.

Hence, A wins C by 200-144 m = 56 m.

Question 2

If in a 300 m race, A can give B 30 m and C 84m, then how many meters can B give C in the same race?

a) 20m b) 40m c) 60m d) 80m

Solution :

Given that, A can give B 30 m.
That is, If A runs 300 m, then B can run (300 - 30 =) 270 m only.

And A can give C 84m means if A runs 300m, then C runs (300 - 84 =) 216 m .

Now, we have

A:B = 300:270 and A:C = 300:216

We have to B:C in 300 m race.

B/C = B/A x A/C
= (270 / 300) x (300 / 216) = (300 / 24 x 10) = 300 / 240

That is, B:C = 300:240

Hence B can give C 300 - 240 = 60m.

Question 3

In a game of 200 points, A can give B 20 points and A can give C 26 points. How many points will B give C in a game of 360 points?

a) 28 b) 12 c) 32 d) 48

Solution :

Given that, A can give B 20 points; that is, A:B = 200:(200-20) = 200:180
And, A can give C 26 points; that is, A:C = 200:(200-26) = 200:174

We have to find B:C in a game of 360 points.

B/C = B/A x A/C = (180 / 200) x (200 / 174) = 180 / 174 = 360 / 348 (since race is for 360m multiply both numerator & denominator by 2)

That is, B:C = 360:348.

Hence B will give C (360-348)= 12 points in 360 points game.

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