## Races and games

#### Races and games

1. 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 ?
1. 39 m
2. 49 m
3. 55 m
4. 25 m

1. 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

##### Correct Option: A

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

1. 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 ?
1. 52 m
2. 75 m
3. 69 m
4. 70 m

1. 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

##### Correct Option: D

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

1. 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 ?
1. 45 m
2. 15 m
3. 25 m
4. 30 m

1. 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

##### Correct Option: D

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

1. In 1 km race, P beats Q by 72 m in 12 s. Find the P's time over the course.
1. 1552/3 s
2. 151 s
3. 1542/3 s
4. 160 s

1. 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

##### Correct Option: C

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

1. X covers 1 km in 8 min 40 s while Y covers the same distance in 10 min. By what distance does X defeat Y?
1. 131/3 m
2. 1332/3 m
3. 1332/5 m
4. 1331/3 m

1. Clearly, X beats Y by 8 s.
Distance covered by Y in 600 s = 1000 m

##### Correct Option: D

Clearly, X beats Y by 8 s.
Distance covered by Y in 600 s = 1000 m
(∵ 10 min = 600 s)
Distance covered by Y 80 s. = (1000/600) x 80 = 400/3 m = 1331/3 m