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11. In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:

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Solution:
B runs452m in 6 sec∴B covers 300m in=(6×245×300)sec=80sec
12. A runs 123 times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

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Solution:
Ratio of speeds of A and B =53:1=5:3
Thus, in race of 5m, A gains 2m over B
2m are gained by A in a race of 5m
80m will be gained by A in a race of
(52×80)m=200 m
∴ Winning post is 200 m away from the starting point
13. In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

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Solution:
A:B=100:75B:C=100:96∴A:C=AB×BC=10075×10096=10072100:72∴AbeatsCby=(100−72)m=28m
14. In a race of 200 m, B can give a start of 10 m to A and C can give a start of 20 m to B. The start that C can give to A in the same race is ?

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Solution:
B : A = 200 : 190
C : B = 200 : 180
=CA=CB×BA=200180×200190=200171
∴ C can give to A, a start of (200 - 171) m = 29 m
15. In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, the time taken by A to run 1 kilometre, is ?

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Solution:
In a km race, suppose A takes t sec,
Then, B takes (t + 30) sec, and C takes (t + 45) sec
180 m is covered by C in 45 sec
∴ 1000 m is covered by C in
= (45180×1000)   sec
= 250 sec
∴ A covers 1000 m in
= (250 - 45) sec
= 205 sec
16. A team played 40 games in a season and won in 24 of them. What percent of games played did the team win ?

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Solution:
Number of games played = 40
Number of won games = 24
Percentage of games played
= (2440×100)
= 60%
17. In a kilometre race, A, B and C are three participants. A can give B start of 50 m and C a start of 69 m. The start which B can allow C, is -

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Solution:
A : B : C
= 1000 : (1000 - 50) : (1000 - 69)
= 1000 : 950 : 931
In a 950 m race, B can give C a start of
(950 - 931) m
= 19 m
In a 1000 m race, B can give C a start of
= (19950×1000)
= 20 m
18. A and B take part in a 100 metres race. A runs at 5 km an hour. A gives B a start of 8 metres and still beats him by 8 seconds. The speed of B is ?

Discuss
Solution:
A's speed = 5 km/hr
= (5×518)  m/sec
= 2518 m/sec
Time taken by A to cover 100 metres
= (100×1825)
= 72 sec
Time taken by B to cover 92 metres
= (72 + 8) sec
= 80 sec
B's speed
9280 m/sec
= (9280×185)  km/hr
= 414100 km/hr
= 4.14 km/hr
19. Four sisters Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs. 32. How much money did Suvarna start with ?

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Solution:
End of Suvarna Tara Uma Vibha
4th Game 32 32 32 32
3rd Game 16 16 16 80
2nd Game 8 8 72 40
1st Game 4 68 36 20
Original
Money 		62 34 18 10

Survarna starts with Rs. 66
20. In a 400 m race, A gives B a start of 5 seconds and beats him by 15 m. In another race of 400 m, A beats B by 717 seconds. Their respective speed are -

Discuss
Solution:
Suppose A covers 400 m in t seconds
Then, B covers 385 m in (t + 5) seconds
∴ B covers 400 m in={(t+5)385×400} sec=80(t+5)77 secAlso, B covers 400 m in=(t+717) sec=(7t+50)7 sec∴80(t+5)77=7t+507⇒80(t+5)=11(7t+50)⇒(80t−77t)=(550−400)⇒3t=150⇒t=50∴ A's speed=40050m/sec=8m/sec∴B's speed=38555m/sec=7m/sec

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