Question 1

In a 400 m race, A runs at a speed of 16 m/s. If A gives B a start of 16 m and still beats him by 40 s, What will be the speed of B?

Accepted Answer

Time taken by A to cover 400 m = Distance/ Speed = 400/16 s = 25 s ∴ B covers (400 -16) = 384 m in(25 + 40) = 65 s ∴ B's speed = 384/65 =5.9 m/s

Question 2

A can run 45 m while B runs 50 m. In a km race B beats A by how many metres?

Accepted Answer

When B runs 50 m, then A runs 45 m. When B runs 1000 m, then A runs (45/50) x 1000 m = 900 m ∴ B beats A by 100 m.

Question 3

A can run 200 m in 35 seconds and B in 38 seconds. By what distance A beats B?

Accepted Answer

The distance covered by B in 35 seconds = 200 x 35 / 38 = 3500 / 19 m Now, 200 – 3500 / 19 = 300 / 19 = 1515⁄19 m Hence, A can beat B by 1515⁄19 m.

Question 4

In a 1000 m race A beats B by 100 m and C by 200 m. By how much can B beats C in a race of 1350 m?

Accepted Answer

If A run 1000 meters then B runs 900 meters and C runs 800 meters. ∴ B runs 1350 meters while C will run 800 * 1350/ 900 = 1200 meters Hence, B can beat C by (1350 – 1200) = 150 m

Question 5

In a game of 100 points A can give B 20 points and C 28 points. How many points can B give C in a game of 100 points?

Accepted Answer

If A Score 100 then B scores 80 and C score 72. ∵ B scores 80 while C scores 72 ∴ B scores 100 while C scores 72 * 100 / 80 = 90 points Hence, in 100 points B can give (100 – 90) = 10 points

Question 6

A can give B 50 m start and C 80 m start in the 1000 m race, how many metres start B give C in a 1000 m race?

Accepted Answer

In a game of 1000 meters, If A scores 1000 meters then B scores 950 meters and C scores 920 meters. ∴ B runs 1000 m while C scores 920 x 1000 / 950= 18400 / 19 m Hence, in 1000 m race, B can give C (1000 - 18400 / 19) = 600 / 19 = 3111⁄19 meters start.

Question 7

In a game of 250 points A can give B 50 points and C 70 points. In the same game how many points can B give C?

Accepted Answer

In a game of 250 points, A scores 250 then B scores 200 points and C scores 180. ∴ B scores 250 points while C scores 180 x 250 / 200 = 225 points Hence, in a game of 250 points B can give C (250 – 225) = 25 points

Question 8

In a race of 300 metres A beats B by 15 metres or 5 seconds. How much time A does take to complete the race?

Accepted Answer

From the question it is clear that speed of B = 15 / 5 = 3 m/s The time taken by B to cover 300 m = 300 / 3 = 100 sec. Hence, time taken by A to complete the race = 100 – 5 = 95 sec.

Question 9

In a Km race A beats B by 25 m or 5 sec. Then find out the time taken by A to complete the race.

Accepted Answer

B runs 25 m in 5 seconds. ∴ B's time to cover 1 Km = 5 x 100 / 25 = 200 sec A's time to cover one Km = 200 - 5 = 195 seconds = 3 minutes 15 seconds.

Question 10

In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?

Accepted Answer

Suppose, P points make the game. Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points. Now, when B scores P points, C scores (P - 15) points. When B scores (P - 20) points, C scores [( P - 15 ) / P * P (P - 20)] points ∴ (P - 15)( P - 20) / P = P - 20 or, P = 100 Hence, 100 points make the game.

Question 11

A runner runs 1 1⁄ 4 laps of a 5 lap race. What fractional part of the race remains to be run?

Accepted Answer

race remains to be run = 5 - 5⁄4 = 15⁄4 .

Question 12

A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet next at the starting …

Accepted Answer

L.C.M. of 252, 308 and 198 = 2772 seconds = 46 × 60 + 12 = 46 min 12 seconds. .

Question 13

Raju runs 1250 meter on Monday and Friday. Another days he runs 1500 meter except for Sunday (He does not run on Sunday). How many kilometer will he run in 3 weeks (first day starting from Monday)?

Accepted Answer

Raju runs on Monday and Friday = 1250 × 2 = 2500 m On Tuesday, Wednesday, Thursday and Saturday, Raju runs 1500 × 4 = 6000 m In 1 week Raju runs 6000 + 2500 = 8500 m In 3 weeks Raju runs 3 × 8500 = 25500 m = 25.5 K

Question 14

In a race of 300 meter, A beats B by 15 meter or 5 sec. A's time over the course is :

Accepted Answer

15 meter is covered by B in 5 sec ∴ 300 meter is covered by B in 5 × 300/15 = 100 seconds ∴ A takes 100 - 5 = 95 seconds.

Question 15

A runs 1 3⁄ 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:

Accepted Answer

The speed of A and B are in the ratio 11 : 8. Let, speeds be 11s and 8s (in m/sec). Let, race be of P meter. Then, time taken by A to run P meter is same as that of B to run (P - 120) meter. ∴ P / 11 = (P - 120) / 8 ∴ P / 11 = (P - 120 / 8 ∴ 8P = 11 x (P - 120 ) ∴ 8P = 11P - 120 x 11 ∴ 11P - 8P = 120 x 11 ∴ 3P = 11 × 120 ∴ P = 440.

Question 16

At 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:

Accepted Answer

In 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 17

In a race of 600 m, A can beat B by 30 m and in a race of 500 m, B can beat C by 25 m. By how many metres will A beat C in a race of of 400 m?

Accepted Answer

If A runs 600 m, then B runs 570 m. If A runs 400 m, B then runs (570/600) x 400 m = 380 m When B runs 500 m, then C runs 475 m, When B runs 380 m, then C runs (475/500) x 380 = 361 m ∴ A beats C by (400 - 361) = 39 m

Question 18

A runs 1% times as fast as B. If A gives B a start of 30 m, how far must the winning post be, so that A and B reach it at the same time?

Accepted Answer

A is 13/4 faster than B. Then, ratio of the rates of A and B = 7 : 4 3 m are gained in a race of 7 m . 30 m are gained in a race of (7/3) x 30 = 70 m

Question 19

In a 250 m race, the ratio of speeds of A and B is 1 : 2, If A has a start of 140 m, then A wins by how many metres?

Accepted Answer

To reach the winning post, A has to cover (250 - 140)m = 110 m From the the ratio of 1 : 2 , When A covers 1m, then B covers 2 m. When A covers 110 m, then B covers ( 2 x 110)m = 220 m ∴ A wins by (250 - 220) = 30 m

Question 20

In 1 km race, P beats Q by 72 m in 12 s. Find the P's time over the course.

Accepted Answer

According to the formula, Time taken by the winner/Distance covered by the loser = Difference of winning time/ Difference of winning distance ⇒ Time taken by P//(1000 - 72) = 12/72 ∴ Time taken by P = (12/72) x 928 = 464/3 = 1542/3 s

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