RACES AND GAMES

Ans .

4 min. 3 s

1. Explanation :

   Clearly, B covers 28 m in 7 seconds.

   B's time over the course = (278 x 1000) sec = 250 seconds.

   A's time over the course = (250 - 7-) sec = 243 sec = 4 min. 3 s

Ans .

196 m

1. Explanation :

   Ratio of the rates of A and B = 7/4 : 1 = 7 : 4.

   So, in a race of 7 m, A gains 3m over B.

   3 m are gained by A in a race of 7 m.

   84 m are gained by A in a race of (7/3 x 84) m = 196 m.

   Winning post must be 196 m away from the starting point

Ans .

50 m

1. Explanation :

   Clearly, A beats B by 10 sec.

   Distance covered by B in 10 sec. = (\(\frac{1000 }{200}\)x 10 )m = 50 m.

   Therefore A beats B by 50 metres

Ans .

5.76 km/hr

1. Explanation :

   Time taken by A to cover 100 m =(60 X 60 / 8000) x 100 sec = 45 sec.

   B covers (100 - 4) m = 96 m in (45 + 15) sec = 60 sec.

   B's speed =\(\frac{96 *60 * 60}{60 *1000} \) km/hr = 5.76 km/hr.

Ans .

936 m

1. Explanation :

   While A covers 1000 m, B covers (1000 - 40) m = 960 m and

   C covers (1000 - 64) m or 936 m.

   When B covers 960 m, C covers 936 m.

Ans .

8 points

1. Explanation :

   A: B = 80 : 75, A : C = 80 : 65.

   B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5

   Therfore ,In a game of 60, B can give C 8 points