A's speed  = `( 5 xx 5/18)` m/sec = `25/18` m/sec

Time taken by A to cover  100 m = `(100 xx 18/25)` sec = 72 sec.

`:.`     Time taken by  B to cover  95 m = ( 72 + 8) sec = 80 sec.

`:.`      B's speed  = `(92/80 xx 18/5)` kmph =  4.14 kmph

A : B = 200 : 169  and  A : C = 200 : 182.

`C/B = (C/A xx A/B) = 182/200 xx 200/169) `  = 182 : 169

When C covers 182 m,  B covers 169 m.

When C covers 350 m,    B covers `(169/182 xx 350)`m = 325 m.

A : B =  100 : 90  and  A : C =  100 : 87

`B/C = B/A xx A/C  = 90/100 xx 100/87 = 30/29`

When  B runs 30 m,  C runs  29 m.

When B runs 180 m ,  C runs `(29/30 xx 180)`m = 174 m

`:.`      B beats C by (180 - 174) m = 6 m.

A : B =  100 : 90  and  A : C =  100 : 72

B : C =  `B/A xx A/C` =  `90/100 xx 100/72 = 90/72`

When B runs 90 m ,  C runs 72 m.

When  B runs  100 m,  C runs  `(72/90 xx 100)`m = 80 m

`:.`     B can give C  20 m.

 A : B  =  100 : 75   and  B : C =  100 : 96.

`:.`      A : C =  `(A/B xx B/C) = ( 100/75 xx 100/96)`

          = `100/72 =   100 : 72`

`:.`     A beats C by  (100 - 72)m =   28 m.

To reach the winning post  A will have to cover a distance of(500 - 140) m    i.e. 360 m.

while A cover  3 m., B cover 4 m.

while A covers 360 m , B cover `(4/3 xx 360)` m = = 480 m.

Thus when  A reached the winning post , B covers 480 m and therefore  remains 20 m. behind .

`:.`       A wins by 20 m.

Ratio of the speeds of A and B  = `5/3 : 1` = 5 : 3

Thus , in a race of 5 m , A gains 2 m  over  B.

2 m are gained by  A in a race of 5 m.

80 m will be gained by  A in a race of `(5/2 xx 80)` m =  200 m.

`:.`      Winning post is 200 m away from the starting point

When  it runs 25 m , A runs `45/2` m.

When B runs 1000 m. A runs `(45/2 xx 1/25 xx 1000)` m  = 900 m.

`:.`      B beats  A by  100 m.

B runs `45/2` m in 6 sec.

`:.`   B  covers  300 m in `(6 xx 2/45 xx 300)`sec. = 80 sec.

B runs 35 m in 7 sec.

`:.`       B covers 200 m in `(7/35 xx 200)) `sec = 40 sec.

B's time over the cours = 40 sec.

`:.`     A's time over the  course = (40 - 7) sec. =  33 sec.