Race & Games

Suggested Lessons

Races & Games

1. Races:
A contest of speed in running, riding, driving, sailing or rowing is called a race.
2. Race Course: The ground or path on which contests are made is called a race course.
3. Starting Point: The point from which a race begins is known as a starting point.
4. Winning Point or Goal: The point set to bound a race is called a winning point or a goal.
5. Winner: The person who first reaches the winning point is called a winner.
6. Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, the race is said to be dead heat race.
7. Start: Suppose A and B are two contestants in a race. If before the start of the race, A is at the starting point and B is ahead of A by 12 metres, then we say that ‘A gives B, a start of 12 metres. To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 – 12) = 88 metres. In a 100 race, A can give B 12 m’ or ‘A can give B a start of 12 m’ or ‘A beats B by 12 m’ means that while A runs 100 m, B runs (100 – 12) = 88 m.

8. 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.

1. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

A. 18 m

 B. 20 m

C. 27 m  

D. 9 m

 Answer: Option B

Explanation:

A : B = 100 : 90.

A : C = 100 : 72.

B : C =\frac{B}{A} ×\frac{A}{C} = \frac{90}{100} × \frac{100}{72} = \frac{90}{72}

When B runs 90 m, C runs 72 m.

When B runs 100 m, C runs\left ( \frac{72}{90}\times100 \right )m= 80 m.

∴B can give C 20 m.

2. A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:

A. 5.15 kmph

B. 4.14 kmph

C. 4.25 kmph

D. 4.4 kmph

Answer: Option B

Explanation:

A’s speed = \left ( 5\times\frac{5}{18} \right )m/sec=\frac{25}{18}m/sec.

Time taken by A to cover 100 m = \left ( 100\times\frac{18}{25} \right )sec= 72 sec.

∴Time taken by B to cover 92 m = (72 + 8) = 80 sec.

∴ B’s speed =\left ( \frac{92}{80}\times\frac{18}{5} \right ) kmph= 4.14 kmph.

3. In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m.Then, A wins by:

A. 60 m

B. 40 m

C. 20 m

D. 10 m

Answer: Option C

Explanation:

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

While A covers 3 m, B covers 4 m. While A covers 360 m, B covers\left ( \frac{4}{3}\times360 \right ) m= 480 m.

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.

∴A wins by 20 m.

4. In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

A. 5.4 m

B. 4.5 m

 C. 5 m

D. 6 m

Answer: Option D

Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

\frac{B}{C} = \frac{B}{A} × \frac{A}{C} =\frac{90}{100} ×\frac{1000}{87} = \frac{30}{29}

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs\left ( \frac{29}{30}\times180 \right )m= 174 m.

∴B beats C by (180 – 174) m = 6 m. .

5.At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?

A. 30 points  

B. 20 points  

C. 10 points

D. 12 points

Answer: Option C

Explanation:

A : B = 60 : 45

A : C = 60 : 40.

∴\frac{B}{C} = \left ( \frac{B}{A}\times\frac{A}{C} \right ) = \left ( \frac{45}{60}\times\frac{60}{40} \right ) =\frac{45}{40}\times\frac{90}{80}= 90 : 80.

∴B can give C 10 points in a game of 90.

6. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

A. 22.75 m

 B. 25 m

 C. 19.5 m

D. {7_{4}}^{7} m

Answer: Option B

Explanation:

A : B = 200 : 169.

A : C = 200 : 182.

\frac{C}{B} = \frac{C}{A}\times\frac{A}{B} =\frac{182}{200}\times\frac{200}{169} = 182 : 169.

When C covers 182 m, B covers 169 m.

When C covers 350 m, B covers \left ( \frac{169}{182}\times350 \right ) m = 325 m.

Therefore, C beats B by (350 – 325) m = 25 m.

7. In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

A. 20 m

B. 25 m

C. 22.5 m  

D. 9 m  

Answer: Option A

Explanation:

Distance covered by B in 9 sec. =\left ( \frac{100}{45}\times9 \right )= 20 m.

∴ A beats B by 20 metres.

8. In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

A. 8 points  

B. 10 points  

C. 14 points

D. 40 points

Answer: Option B

Explanation:

A : B = 100 : 80. A : C = 100 : 72.

∴ \frac{B}{C} = \left ( \frac{B}{A}\times\frac{A}{C} \right )= \left ( \frac{80}{100}\times\frac{100}{72} \right ) = \frac{10}{9} = \frac{100}{90} = 100 : 90.

∴B can give C 10 points.

9. In a 200 metres race A beats B by 35 m or 7 seconds. A’s time over the course is:

A. 40 sec

B. 47 sec

C. 33 sec

D. None of these

 Answer: Option C

Explanation:

B runs 35 m in 7 sec.

∴B covers 200 m in \left ( \frac{7}{35}\times200 \right )= 40 sec.

B’s time over the course = 40 sec.

∴A’s time over the course (40 – 7) sec = 33 sec.

10. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:  

A. 100 m

B. {111_{9}}^{1} m

C. 25 m

D. 50 m

Answer: Option A

Explanation:

When B runs 25 m, A runs \frac{45}{2} m When B runs 1000 m, A runs \left ( \frac{45}{2}\times\frac{1}{25}\times1000 \right )m = 900 m.

∴B beats A by 100 m.

11. In a 300 m race A beats B by 22.5 m or 6 seconds. B’s time over the course is:

A. 86 sec  

B. 80 sec

C. 76 sec

D. None of these

Answer: Option B

Explanation:

B runs \frac{45}{2}  m in 6 sec.

∴B covers 300 m in \left ( 6\times\frac{45}{2}\times300 \right )sec= 80 sec.

12. 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?

A. 200 m

B. 300 m  

C. 270 m

D. 160 m

Answer: Option A

Explanation:

Ratio of the speeds of A and B =\frac{5}{3}: 1 = 5 : 3.

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

80 m will be gained by A in race of\left ( \frac{5}{2}\times80 \right )m = 200 m.

∴Winning post is 200 m away from the starting point.

13. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

A. 21 m

B. 26 m

 C. 28 m

  D. 29 m

Answer: Option C

Explanation:

A : B = 100 : 75

B : C = 100 : 96.

∴A : C =\left ( \frac{A}{B}\times\frac{B}{C} \right ) =\left ( \frac{100}{75}\times\frac{100}{96} \right ) =\frac{100}{72} = 100 : 72.

∴A beats C by (100 – 72) m = 28 m.

Series – Odd Man Out

1. 3, 5, 11, 14, 17, 21 A. 21

        B. 17

        C. 14

         D. 3

Answer: Option C

Explanation:

Each of the numbers except 14 is an odd number. The number ’14’ is the only EVEN number.

2. 8, 27, 64, 100, 125, 216, 343 A. 27

        B. 100

       C. 125

       D. 343

   Answer: Option B

Explanation:

The pattern is  2^{3},  3^{3},  4^{3},  5^{3},  6^{3}, 7^{3}. But, 100 is not a perfect cube.

3. 10, 25, 45, 54, 60, 75, 80 A. 10

      B. 45

      C. 54

      D. 75

Answer: Option C

Explanation:

Each of the numbers except 54 is multiple of 5.

4. 396, 462, 572, 427, 671, 264 A. 396

       B. 427

        C. 671

        D. 264

Answer: Option B

Explanation:

In each number except 427, the middle digit is the sum of other two.

5. 6, 9, 15, 21, 24, 28, 30  

A. 28

B. 21

C. 24

D. 30

Answer: Option A

Explanation:

Each of the numbers except 28, is a multiple of 3.

6. 1, 4, 9, 16, 23, 25, 36    

 A. 9

B. 23

C. 25

D. 36

Answer: Option B

Explanation:

Each of the numbers except 23, is perfect square.

7. 1, 4, 9, 16, 20, 36, 49

A. 1

B. 9

C. 20

D. 49

Answer: Option C

Explanation:

The pattern is  1^{2},  2^{2},  3^{2},  4^{2},  5^{2},  6^{2}, 7^{2}. But, instead of 5^{2}, it is 20 which to be turned out.

8. 2, 5, 10, 17, 26, 37, 50, 64

A. 50

B. 26

C. 37

D. 64

Answer: Option D

Explanation:

(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1 But, 64 is out of pattern.

9. 10, 14, 16, 18, 21, 24, 26

A. 26

B. 24

C. 21

D. 18

Answer: Option C

Explanation:

Each of the numbers except 21 is an even number.

10. 16, 25, 36, 72, 144, 196, 225  

A. 36

B. 72

C. 196

D. 225

Answer: Option B

Explanation:

Each of the numbers except 72 is a perfect square.

11. 331, 482, 551, 263, 383, 362, 284

A. 263

B. 383

C. 331

D. 551

Answer: Option B

Explanation:

In each number except 383, the product of first and third digits is the middle one.

12. 835, 734, 642, 751, 853, 981, 532

A. 751

B. 853

C. 981

D. 532

Answer: Option A

Explanation:

In each number except 751, the difference of third and first digit is the middle one.

13. 41, 43, 47, 53, 61, 71, 73, 81

A. 61

B. 71

C. 73

D. 81

Answer: Option D

Explanation:

Each of the numbers except 81 is a prime number.

14. 3, 5, 7, 12, 17, 19 A. 19

        B. 17

        C. 5

        D. 12

Answer: Option D

Explanation:

Each of the numbers is a prime number except 12.

Series – Find Missing Number 1. 16, 33, 65, 131, 261, (….)

A. 523

B. 521

C. 613

D. 721

Answer: Option A

Explanation:

Each number is twice the preceding one with 1 added or subtracted alternatively. So, the next number is (2 x 261 + 1) = 523. 2. 10, 5, 13, 10, 16, 20, 19, (….)

A. 22

B. 40

C. 38

D. 23

Answer: Option B

Explanation:

There are two series (10, 13, 16, 19) and (5, 10, 20, 40), one increasing by 3 and the other multiplied by 2. 3. 1, 4, 9, 16, 25, 36, 49, (….)

A. 54

B. 56

C. 64

D. 81

Answer: Option C

Explanation:

Numbers are  1^{2},  2^{2},  3^{2},  4^{2},  5^{2},  6^{2},  7^{2} So, the next number is  8^{2} = 64. 4. 2, 4, 12, 48, 240, (….)

A. 960

B. 1440  

C. 1080

 D. 1920

Answer: Option B

Explanation:

Go on multiplying the given numbers by 2, 3, 4, 5, 6. So, the correct next number is 1440. 5. 8, 7, 11, 12, 14, 17, 17, 22, (….)  

A. 27

 B. 20  

C. 22  

D. 24

Answer: Option B

Explanation:

There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively. 6. 11, 13, 17, 19, 23, 29, 31, 37, 41, (….)

A. 43

B. 47

C. 53

D. 51

Answer: Option A

Explanation:

Numbers are all primes. The next prime is 43. 7. 8, 24, 12, 36, 18, 54, (….)

A. 27  

B. 108

C. 68

D. 72 Answer: Option A

Explanation:

Numbers are alternatively multiplied by 3 and divided by 2. So, the next number = 54 ÷ 2 = 27. 8. 2, 6, 12, 20, 30, 42, 56, (….)

A. 61

B. 64

 C. 72

D. 70

Answer: Option C

Explanation:

The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8. So, the next number is 8 x 9 = 72. 9. 4, -8, 16, -32, 64, (….)

A. 128

B. -128

C. 192  

D. -192

Answer: Option B

Explanation:

Each number is the proceeding number multiplied by -2. So, the required number is -128. 10. 7, 26, 63, 124, 215, 342, (….)

A. 481

B. 511  

C. 391

D. 421

Answer: Option B

Explanation:

Numbers are ( 2^{3} – 1), ( 3^{3}– 1), ( 4^{3}– 1), ( 5^{3}– 1), ( 6^{3}– 1), ( 7^{3}– 1) etc. So, the next number is ( 8^{3}– 1) = (512 – 1) = 511. 11. 5, 10, 13, 26, 29, 58, 61, (….)  

A. 122

B. 64

C. 125

D. 128

Answer: Option A

Explanation:

Numbers are alternatively multiplied by 2 and increased by 3. So, the missing number = 61 x 2 = 122. 12. 15, 31, 63, 127, 255, (….)

A. 513

B. 511

C. 517

D. 523

Answer: Option B

Explanation:

Each number is double the preceding one plus 1. So, the next number is (255 x 2) + 1 = 511. 13. 1, 8, 27, 64, 125, 216, (….)

A. 354

B. 343

C. 392

D. 245

Answer: Option B

Explanation:

Numbers are  1^{3},  2^{3},  3^{3},  4^{3},  5^{3},  6^{3} So, the missing number is  7^{3} = 343. 14. 3, 7, 6, 5, 9, 3, 12, 1, 15, (….)

A. 18

B. 13

C. -1

D. 3

Answer: Option C

Explanation: There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted. The next number is 1 – 2 = -1.