**BASICS OF RACES AND GAMES:**Problems on Races and Games are asked a number of times in competitive exams.let us Start learning basics of Races and Games.

If P and Q are participating in a race such that . If P is at the starting point and Q is ahead of P by 16 metres, then we can say "P has given Q a start of 16 metres".

In this situation If race is of length 100 meter, then P has to cover 100 metres , while Q has to cover ( 100 - 16 ) = 84 metres.

Here for a race of 100 metres all these statements are equivalent:

" P beats Q by 16m " or " P gives Q a start of 16m " or " P can give Q 16m "

Games : In a game of 100 if P scores 100 points first then he will be winner

If P scores 100 points and Q scores 85 only then we can say " P has given 15 points to Q "

**Ex. P runs 5/3 times fast than Q. If P has given Q a start of 96 m, What should be the distance of running post so that P and Q reach it at the same time ?**

Solution : Rate of A and B = 5/3 : 1 = 15 : 3

From the ratio 15 : 3 we conclude that in a race of 15 m, P gains 12 m more than Q

12 m are being gained by P in a race of 15 m

1 m eing gained by P in a race of 15/12

**96 m gained by P in a race of =(15/12)x96 = 120m.**

So both P and Q will reach at same time when post will be 120 m

**Ex. P can run a 900 m distance in 2 min and Q can cover the same distance in 2 min. 30 sec. By how much distance P beat Q ?**

Solution: Here Q takes 30 seconds more than P to cover the same distance.

**Distance covered by Q in 30 sec = (900/150) x 30 = 180 m.**

So, P beats Q by 180 m

**Ex. P and Q take part in a 100 m race. P runs at 6 km/hr. P gives Q a start of 8 m and still beats him by 12 seconds. Find out the speed of Q.**

Solution : Since P runs 100 m and speed is 6*(5/18)= 5/3 m/sec

**Time taken by P to run 100 m =(100/5) x 3 = 60 sec.**

Since P has given Q start of 8 m and beats by 12 sec then , Q will cover 92 m in 72 sec ,

**So speed of Q is = (92/72) x (18/5) =23/5=4.6 km/hr**

**Ex. In a 100 m race , P beat Q by 10 m and R by 15 m . In a race of 180 m, Q will beat R by ?**

Solution : Since P : Q = 100 : 90 and P : R = 100 : 85 So,

**Q/R = (Q/P)x(P/R) = (90/100) x (100/85) = 18/17**

When Q travels 18 m then R travels 17 m, When Q travels 180 m then R travels :

**(17/18) x 100 = 170 m, so Q beats R by (180 - 170) = 10 m.**

**Ex. In a game of 90 points, A can give B 10 points and C 15 points. Then how any points B can give C in a game of 80 ?**

Solution : A : B = 90 : 80 , A : C = 90 : 75

**(B/A) x (A/C) =B/C = (80/90) x (90/75) =80/75**

So in a game of 80 B will give 5 points to C