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**Name: **Race and Games – Aptitude Practice Test – 3

**Subject: **Aptitude

**Topic: **Race and Games Problems

**Questions: **9 Objective type

**Time Allowed: **18 Minutes

**Important for: **RBI, SBI and IBPS Bank exams, SSC CGL, State Competitions, Army, CRPF, BSF and Job aptitude test etc.

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- Question 1 of 9
##### 1. Question

1 pointsIn a race of 600 meter, A can beat B by 60 meter and in a race of 500 meter, B can beat C by 50 meter. By how many meters will A beat C in a race of 400 meter?

CorrectIf A runs 600 meter, B runs 600 – 60 or, 540 meter.

If A runs 400 meter, B runs = (540 × 400) / 600 = 360 meter.

Now, when B runs 500 meter, C runs 500 – 50 = 450 meter

∴ When B runs 360 meter, C runs = (450 × 360) / 500 = 324 meter.IncorrectIf A runs 600 meter, B runs 600 – 60 or, 540 meter.

If A runs 400 meter, B runs = (540 × 400) / 600 = 360 meter.

Now, when B runs 500 meter, C runs 500 – 50 = 450 meter

∴ When B runs 360 meter, C runs = (450 × 360) / 500 = 324 meter. - Question 2 of 9
##### 2. Question

1 pointsIn a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?

CorrectWhen A scores 75 points, B scores 50 points.

When A scores 90 points, C scores (90 – 18) = 72 points.

∴ When A scores 75 points, C scores = (72/90)×75 = 60 points

A : B : C = 75 : 50 : 60

C : B = (60 / 50) = (120 / 100).IncorrectWhen A scores 75 points, B scores 50 points.

When A scores 90 points, C scores (90 – 18) = 72 points.

∴ When A scores 75 points, C scores = (72/90)×75 = 60 points

A : B : C = 75 : 50 : 60

C : B = (60 / 50) = (120 / 100). - Question 3 of 9
##### 3. Question

1 pointsA and B run a 5 kilometer race on a round course of 400 meter. If their speeds be in the ratio 5 : 4, then how often does the winner pass the other?

CorrectWhen A makes 5 rounds, B makes 4 rounds.

In order to pass each other, the difference in number of rounds made by each must be one. Here, A passes B each time, when A makes 5 rounds.

Distance covered by A is 5 rounds = [(5 × 400)/ 100] = 2 kilometer.

In covering 2 kilometer, A passes B one time.

∴ In covering 5 kilometer, A passes B = (5/2) = 2.5 times.IncorrectWhen A makes 5 rounds, B makes 4 rounds.

In order to pass each other, the difference in number of rounds made by each must be one. Here, A passes B each time, when A makes 5 rounds.

Distance covered by A is 5 rounds = [(5 × 400)/ 100] = 2 kilometer.

In covering 2 kilometer, A passes B one time.

∴ In covering 5 kilometer, A passes B = (5/2) = 2.5 times. - Question 4 of 9
##### 4. Question

1 pointsIn a 500 meter race, the ration of speeds of two contestants A and B is 3 : 4. A has a start of 140 meter. Than, A wins by;

CorrectTo reach the winning post, A will have to cover a distance of (500 – 140), i.e., 360 meter.

While A covers 3 meter, B covers [(4/3) ×360] = 480 meter.

So, A reaches the winning post while B remains 20 meter behind.

∴ A wins by 20 meter.IncorrectTo reach the winning post, A will have to cover a distance of (500 – 140), i.e., 360 meter.

While A covers 3 meter, B covers [(4/3) ×360] = 480 meter.

So, A reaches the winning post while B remains 20 meter behind.

∴ A wins by 20 meter. - Question 5 of 9
##### 5. Question

1 pointsIn a Kilometer race A beats B 100 meter C by 200 meter. By how many can B beat C in a race of 1350 meter?

CorrectWhile A runs 1000 meter,

B runs 1000 – 100 = 900 meter,

and C runs 1000 – 200 = 800 meter.

∴ While B runs 900 meter; C runs = 800 meter.

∴ While B runs 1350 meter ; C runs = [(800/900)×1350] = 1200 meter

∴ B can beat C by 1350 – 1200 = 150 meter.IncorrectWhile A runs 1000 meter,

B runs 1000 – 100 = 900 meter,

and C runs 1000 – 200 = 800 meter.

∴ While B runs 900 meter; C runs = 800 meter.

∴ While B runs 1350 meter ; C runs = [(800/900)×1350] = 1200 meter

∴ B can beat C by 1350 – 1200 = 150 meter. - Question 6 of 9
##### 6. Question

1 pointsTwo boys, A and B at 9.2 and 6 kilometer an hour. A having 190 meter start. The course being 1 kilometer, B wins by a distance of

CorrectSpeeds (in meter/seconds) of A is = (9/2)× (5/18) = (5/4)

Speeds (in meter/seconds) of B is = 6 × (5/18) = (5/3)

A has a start of 190 meter. So, A has to run 1000 – 190 = 810 meter, while B 1000 meter.Time taken by B to cover 1000 meter = (3/5) × 1000 = 600 seconds.

In this time, A covers = (5/4)×600 = 750 meter

So, B reaches the winning post while A remains 810 – 750 = 60 meter behind.

∴ B wins by 60 meter.IncorrectSpeeds (in meter/seconds) of A is = (9/2)× (5/18) = (5/4)

Speeds (in meter/seconds) of B is = 6 × (5/18) = (5/3)

A has a start of 190 meter. So, A has to run 1000 – 190 = 810 meter, while B 1000 meter.Time taken by B to cover 1000 meter = (3/5) × 1000 = 600 seconds.

In this time, A covers = (5/4)×600 = 750 meter

So, B reaches the winning post while A remains 810 – 750 = 60 meter behind.

∴ B wins by 60 meter. - Question 7 of 9
##### 7. Question

1 pointsAt a game of billiards, A can give B 6 points in 50 and he can give C 13 in 65. In a game of 55, number of points B can give C is:

CorrectIn a game of 50.

∴ While A scores 50, B scores 50 – 6 = 44 and in a game of 65.

While A scores 65, C scores 65 -13 = 52

∴ While A scores 50, C scores = (52 / 65) × 50 = 40.

∴ While B scores 44, C’s score = 40

While B scores 55, C’s score = (40 / 44) × 55 = 50.

∴ In a game of 55.

B can give C 55- 50 = 5 points.IncorrectIn a game of 50.

∴ While A scores 50, B scores 50 – 6 = 44 and in a game of 65.

While A scores 65, C scores 65 -13 = 52

∴ While A scores 50, C scores = (52 / 65) × 50 = 40.

∴ While B scores 44, C’s score = 40

While B scores 55, C’s score = (40 / 44) × 55 = 50.

∴ In a game of 55.

B can give C 55- 50 = 5 points. - Question 8 of 9
##### 8. Question

1 pointsIn a Kilometer race A can beat B by 80 meter can beat C by 60 meter. In the same race, A can beat C by:

CorrectWhile A runs 1000 meter, B runs 1000 – 80 = 920 meter

and while B runs 1000 meter, C runs 1000-60 = 940 meter

∴ While B runs 920 meter;

C runs = (940 / 1000) × 920 = 4324 / 5 meter

∴ While A runs 1000 meter, C runs 4324 / 5 meter.

∴ A can beat C by 1000 – (4324 / 5) = (676 / 5) meter.IncorrectWhile A runs 1000 meter, B runs 1000 – 80 = 920 meter

and while B runs 1000 meter, C runs 1000-60 = 940 meter

∴ While B runs 920 meter;

C runs = (940 / 1000) × 920 = 4324 / 5 meter

∴ While A runs 1000 meter, C runs 4324 / 5 meter.

∴ A can beat C by 1000 – (4324 / 5) = (676 / 5) meter. - Question 9 of 9
##### 9. Question

1 pointsIn a game of 90 points, A can give B 15 points and C 30 points. How many points can B give C in a game of 100 points?

CorrectA : B : C = 90 : 75 : 60

B : C = (75 / 60) = (70 × 100 / 75) / (60 × 100 / 75) = 100 / 80

Hence, in a game of 100 points, B can give C (100 – 80) = 20 points.IncorrectA : B : C = 90 : 75 : 60

B : C = (75 / 60) = (70 × 100 / 75) / (60 × 100 / 75) = 100 / 80

Hence, in a game of 100 points, B can give C (100 – 80) = 20 points.