Races and games
 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 ?

 39 m
 49 m
 55 m
 25 m

View Hint View Answer Discuss in Forum
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 mCorrect 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
 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 ?

 52 m
 75 m
 69 m
 70 m

View Hint View Answer Discuss in Forum
A is 1^{3}/_{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 mCorrect Option: D
A is 1^{3}/_{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
 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 ?

 45 m
 15 m
 25 m
 30 m

View Hint View Answer Discuss in Forum
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 mCorrect 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
 In 1 km race, P beats Q by 72 m in 12 s. Find the P's time over the course.

 155^{2}/_{3} s
 151 s
 154^{2}/_{3} s
 160 s

View Hint View Answer Discuss in Forum
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) = 12/72Correct 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 = 154^{2}/_{3} s
 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?

 13^{1}/_{3} m
 133^{2}/_{3} m
 133^{2}/_{5} m
 133^{1}/_{3} m

View Hint View Answer Discuss in Forum
Clearly, X beats Y by 8 s.
Distance covered by Y in 600 s = 1000 mCorrect 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 = 133^{1}/_{3} m