Question 1

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

Accepted Answer

B runs 45 m in 6 sec. 2 ∴ B covers 300 m in ❨ 6 x 2 x 300 ❩sec = 80 sec. 45

Question 2

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

Accepted Answer

B runs 35 m in 7 sec. ∴ B covers 200 m in ❨ 7 x 200 ❩ = 40 sec. 35 B's time over the course = 40 sec. ∴ A's time over the course (40 - 7) sec = 33 sec.

Question 3

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

Accepted Answer

A : B = 100 : 90. A : C = 100 : 72. B : C = B x A = 90 x 100 = 90 . A C 100 72 72 When B runs 90 m, C runs 72 m. When B runs 100 m, C runs ❨ 72 x 100 ❩m = 80 m. 90 ∴ B can give C 20 m.

Question 4

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

Accepted Answer

When B runs 25 m, A runs 45 m. 2 When B runs 1000 m, A runs ❨ 45 x 1 x 1000 ❩m = 900 m. 2 25 ∴ B beats A by 100 m.

Question 5

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:

Accepted Answer

A : B = 200 : 169. A : C = 200 : 182. C = ❨ C x A ❩ = ❨ 182 x 200 ❩ = 182 : 169. B A B 200 169 When C covers 182 m, B covers 169 m. When C covers 350 m, B covers ❨ 169 x 350 ❩m = 325 m. 182 Therefore, C beats B by (350 - 325) m = 25 m.

Question 6

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:

Accepted Answer

A : B = 100 : 75 B : C = 100 : 96. ∴ A : C = ❨ A x B ❩ = ❨ 100 x 100 ❩ = 100 = 100 : 72. B C 75 96 72 ∴ A beats C by (100 - 72) m = 28 m.

Question 7

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:

Accepted Answer

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 ❨ 4 x 360 ❩m = 480 m. 3 Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind. ∴ A wins by 20 m.

Question 8

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:

Accepted Answer

A's speed = ❨ 5 x 5 ❩m/sec = 25 m/sec. 18 18 Time taken by A to cover 100 m = ❨ 100 x 18 ❩sec = 72 sec. 25 ∴ Time taken by B to cover 92 m = (72 + 8) = 80 sec. ∴ B's speed = ❨ 92 x 18 ❩kmph = 4.14 kmph. 80 5

Question 9

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?

Accepted Answer

A : B = 60 : 45. A : C = 60 : 40. ∴ B = ❨ B x A ❩ = ❨ 45 x 60 ❩ = 45 = 90 = 90 : 80. C A C 60 40 40 80 ∴ B can give C 10 points in a game of 90.

Question 10

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:

Accepted Answer

A : B = 100 : 90. A : C = 100 : 87. B = B x A = 90 x 100 = 30 . C A C 100 87 29 When B runs 30 m, C runs 29 m. When B runs 180 m, C runs ❨ 29 x 180 ❩m = 174 m. 30 ∴ B beats C by (180 - 174) m = 6 m.

Question 11

A runs 1⅔ 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?

Accepted Answer

Ratio of the speeds of A and B = 5 : 1 = 5 : 3. 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 ❨ 5 x 80 ❩m = 200 m. 2 ∴ Winning post is 200 m away from the starting point.

Question 12

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

Accepted Answer

A : B = 100 : 80. A : C = 100 : 72. ∴ B = ❨ B x A ❩ = ❨ 80 x 100 ❩ = 10 = 100 = 100 : 90. C A C 100 72 9 90 ∴ B can give C 10 points.

Question 13

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

Accepted Answer

Distance covered by B in 9 sec. = ❨ 100 x 9 ❩m = 20 m. 45 ∴ A beats B by 20 metres.

Question 14

Raman covers 1 km in 8 min while suman covers the same distance in 10 min. By what distance does Raman beat Suman?

Accepted Answer

Raman covers 1 km in 8 min and suman cover 1 km in 10 min. If they starts together, then distance covered by suman in 8 min = (1000/10) x 8 = 800 m ∴ Raman will beat suman by (1000 - 800 ) m = 200 m

Question 15

In a race of 150 m, A gives B a start of 20 m. What distance will be covered by B?

Accepted Answer

Required distance = (150 - 20) m = 130 m

Question 16

In a race, P gives Q a start of 25 m making length of race for Q a distance of 175 m. Find the total length of race.?

Accepted Answer

Required length = (175 + 25)m = 200 m

Question 17

In a 800 m race, A gives some start to B and this makes the length of race for B 725 m. What start does B get from A?

Accepted Answer

Start given by A to B = (800 - 725)m = 75 m

Question 18

In a game of 100 points, A scores 100 points while B scores only 65 points. In this game, how much points can A give to B?

Accepted Answer

Score of A = 100 points Score of B = 65 points ∴ A can give (100 - 65 ) = 35 points to B.

Question 19

In 1 km race, A beats B by 18 m or 9 s. Find the A' s time over the course.

Accepted Answer

Clearly, B covers 18 m in 9 s. ∴ B's time over the course = 9/18 x 1000 = 500 s ∴ A' s time over the course = (500 - 9) = 491 s

Question 20

In a 1000 m race, X beats Y by 140 m or 14 s. What will be the X's time over the course?

Accepted Answer

Clearly, Y covers 140 m in 14 s ∴ Y' s time over the course = (14/140) x 1000 = 100 s ∴ X' s time over the course = 100 - 14 = 86 s

Races and Games Questions