Question 1

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

Accepted Answer

When 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 in 5 rounds = 5 * 400 / 100 × = 2 Km. In covering 2 Km, A passes B 1 time. ∴ In covering 5 Km, A passes B = 5 / 2 = 21⁄2 times.

Question 2

A and B runs a Km race. If A gives B a start of 50 m, A wins by 14 sec and, if A gives B a start of 22 sec Km, B wins by 20 m. The time taken by A to run a Km is:

Accepted Answer

Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively. When B gets a start of 50 m, B runs. 1000 - 50 = 950 m while A runs 1000 m. ∴ 950 / 100 Q - P = 14, i.e., 0.95Q - P = 14 …(1) and, when B gets a start of 22 seconds, A runs for (Q - 22) seconds, while B runs for Q seconds. ∴ 1000 - 1000 / P (Q - 22) = 20 i.e., 50Q - 49P = 1100. …(2) Multiplying Eq. (1) by 49 and subtract from Eq. (2) 3.45Q = 414 ∴ Q= 120 sec. ∴ from (1) ⇒ P = 0.95 × 120 - 14 = 100 seconds.

Question 3

A and B start from the same point and run around a circular stadium, whose circumference is 4200 m, at the rate of 500 m and 700 m per minute respectively, in the opposite directions. They will meet each other in :

Accepted Answer

Let us assume A cover P meter in the time after which he meets with B. According to question, Time taken by A to cover the P distance = Time taken by B to cover the 4200 - P distance. Use the distance and time formula P / 500 = (4200 - P ) / 700 Or 700P = 500 x 4200 - 500P Or 700P + 500P = 500 x 4200 Or 1200P = 500 x 4200 Or 12P = 5 x 4200 Or P = 5 x 4200 / 12 Or P = 5 x 350 Or P = 1750 meters Required time taken by A to cover 1750 meters = 1750 / 500 = 175/50 Required time taken by A to cover 1750 meters = 3.5 minutes.

Question 4

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

Accepted Answer

A scores 100 while B scores 100 - 20 = 80 and C scores 100 - 28 = 72. ∴ While B scores 80, C scores 72. ∴ While B scores 100, C scores 72 × 100 / 80 = 90. ∴ B can give C 100 - 90 = 10 points.

Question 5

In 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?

Accepted Answer

A : B : C = 90 : 75 : 60 B:C = 75 / 60 = ( 75 x 100⁄75 ) / ( 60 x 100⁄75) = 100 / 80 Hence, in a game of 100 points, B can give C(100 - 80) = 20 points.

Question 6

The respective ratio between the speeds of a car, a train and a bus is 5 : 9 : 4. The average speed of the car, the bus and the train is 72 Km/h together. What is the average speed of the car and the train together?

Accepted Answer

Total speed of car, bus and train = 72 × 3 = 216 Km Speed of car and train = ( 5 + 9 ) x 216 / ( 5 + 9 + 4 ) = 168 Km Average = 168 / 2 = 84 Km

Question 7

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/C = (B/A*A/C) = (90/100*100/87) = 30/29 When B runs 30 m, C runs 29 m. When B runs 180 m, C runs (29/30*180)m =174m B beats C by (180 - 174) m = 6 m.

Question 8

In a 1 km race, A beats B by 28 meters in 7sec. Find A's time over the course?

Accepted Answer

B covers 28 meters in 7sec. So, B's time over the course = (7/28)*100 =250 sec. Whereas A's time over the course = 250 -7 = 243 sec. i.e A's time over the course is 4min , 3 sec.

Question 9

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 45/2 m When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m. B beats A by 100 m.

Question 10

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*5/15)m/sec = (25/18)m/sec Time taken by A to cover 100 m = (100*18/15)sec = 72sec Time taken by B to cover 92 m = (72 + 8) = 80 sec. B's speed =(92/80*18/5)kmph =4.14kmph

Question 11

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. = (100/45)*9m = 20m A beats B by 20 metres.

Question 12

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 (4/3)*360 = 480 m. Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind. A wins by 20 m.

Question 13

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 (7/35*200) = 40 sec. B's time over the course = 40 sec. A's time over the course (40 - 7) sec = 33 sec.

Question 14

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/C = (B/A*A/C) = (45/60*60/45) = 45/40 = 90/80 = 90:80 B can give C 10 points in a game of 90.

Question 15

In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ?

Accepted Answer

When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m. When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m. In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C. In a race of 600 m, the number of meters by which A beats C = (600 x 212.5)/1000 = 127.5 m.

Question 16

A runs 123 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 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 2 * 80 m =200m => Winning post is 200 m away from the starting point.

Question 17

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/B = (C/A*A/B) = (182/200*200/169) = 182:169 When C covers 182 m, B covers 169 m. When C covers 350 m, B covers (169/180*350)m = 325 m Therefore, C beats B by (350 - 325) m = 25 m.

Question 18

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

28m

Question 19

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

Accepted Answer

10 points

Question 20

In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?

Accepted Answer

When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters. So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C. So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.

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