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
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.
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
Since P has given Q start of 8 m and beats by 12 sec then , Q will cover 92 m in 72 sec ,
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,
When Q travels 18 m then R travels 17 m, When Q travels 180 m then R travels :
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
So in a game of 80 B will give 5 points to C
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