Races and Games Practice Test 1 with solutions

Let the distance be = x metre
Distance run by A = x metre
Distance run by B = (x - 20) metres.
B can beat C by 10 metres
Distance run by C = (x - 10) metres
Distance run by A can beat by 28 metres
Distance run by C = (x - 28) metres
Distance run by B = x -20
Distance run by C = $\left(\frac{\mathit{x}\times 10}{\mathit{x}}\right)\times \left(\mathit{x}-20\right)$
‘A’ can beat C by 28 metres
$\mathit{x}-\left[\frac{\left(\mathit{x}-10\right)\left(\mathit{x}-20\right)}{\mathit{x}}\right]$ = 28
${\mathit{x}}^2-{\mathit{x}}^2$ + 30x - 200 = 28x
30x - 200 = 28x
2x = 200
x = 100 metres