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1) In a kilometer race, A beats B by 40 meters or by 5 seconds. What is the time taken by A over the course?

A runs 1km = 1000 m, it means B runs 1000 – 40 = 960 meters Time is taken by B for 40 meters = 5 seconds Time is taken by B for 960 meters = × 960=120 seconds

The time in which B covered 960 meters, A has covered 1000 meters. ∴ A’s time over the course = 120 seconds = 2 minutes

2) In a race of 600 m, A can beat B by 50 m, and in another race of 500 m, B can beat C by 60 m. Then by how many meters will A beat C in a race of 400 meters?

When A runs 600 m, Then B runs (600 – 50) = 550 m Now, When B runs 500 m, Then C runs (500 – 60) = 440 m When B runs 550 m then C runs =(440*550)/500 = 484 m

When A runs 600 m then C runs 484 m,

Now in a 400 meters race, when A runs 400 runs, C will run: 484/600 * 400 = 968/3 m ∴ A beats C in a 400 m race by

(400-(968/3))=(1200-968)/3 =232/3 =77 1/3 m

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

To reach the winning point, A has to cover a distance of (500 – 140) = 360 m According to the question When A covers 3 m, then B covers 4 m And when A covers 360 m, then B covers (4/3 * 360)= 480 m Thus, when A reaches the winning point, B covers 480 m and remains 20 m behind. Therefore A wins from B by 20 m.

4) A can run 22.5 m while B runs 25 m. In a one kilometer race, B beats A by

When A makes 100 points, B makes (100 – 20) = 80 Points and C makes (100 – 28) = 72 points So, when B makes 80 points, C makes 72 points. ∴ When B makes 100 points then C makes 72/80 *100 =90 points ∴ B can give C 10 points in a game of 100 points.

7) A, B, and C are three contestants in a one kilometer race. If A can give B a start of 40 m and A can give a start of 64 m, how many meters? start can B give C?

While A covers 1000 m, B covers (1000 – 40) m = 960 m And C covers (1000 – 64) m = 936 m. When B covers 960 m, C covers 936 m. When B covers 1000 m, C covers =(936/960 *1000)= 975 m ∴ B can give C a start of (1000 – 975) = 25 m.

8) Three men A, B and C walk around a circle, 1760 meters in circumference, at the rates of 160 meters, 120 meters and 105 meters per minute respectively. If they all start together and walk in the same direction, when will they be first together again?

To gain 40 meters over B, A takes 1 minute. To gain 1760 meters over B, A takes: (1/40 * 1760) = 44 minutes Again, to gain 55 meters over C, A takes 1 min. ∴To gain 1760 meters over C, A takes (1/55 * 1760 = 32 min Thus, A and B will be together after 44 minutes, while A, and C are together again after 32 minutes. Now, LCM of 44 and 32 is 352. So, A, B, and C will be first together again after 352 minutes.

9) In a game of billiards, A can give B 12 points in a game of 60 points and A can give C 10 points in a game of 90 points. How many points can C give B in a game of 70?

If A scores 60 points, B scores 48 points. Also, if A scores 90 points, C scores 80 points. A: B = 60:48 and A: C = 90:80 B: C = (A/C) * (B/A) = (90/80) * (48 /60) = 9/10 When C scores 10 points B scores 9 points. So, When C scores 70 points B scores = (9/10) * 70 = 63 points

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

Distance covered by B in 45 seconds = 100 meters Distance covered by B in 9 seconds = (100/45) * 9 = 20 meters So, when A covers 100 meters in 36 seconds, B was 20 meters away from the winning post. Thus, A beats B by 20 meters.