Madeeasy workbook

Question

In a $200m$ race, $A$ beats $B$ by $20m$.$B$ beates $C$ by $10m$ in a $250m$ race.By how many meters will $A$ beat $C$ in a $1 km$ race?

Answer 1

In a 200 m race A beats by B by 20m,

$∴ A:B = 200 : (200-20) = 200:180$

$∴ B:C = 250 : (250-10) = 250:240$

$∴ \dfrac{A}{B} \times \dfrac{B}{C} = \dfrac{200}{180} \times \dfrac{250}{240} = \dfrac{A}{C} = \dfrac{125}{108}$

∴ When A covers 125m , C covers 108 m

Or, when A covers 1000m (1km) C covers $\dfrac{108}{125}\times 1000 = 864 m$

$\color{green}{\text{∴ A beats C by (1000 - 864)m =}}$ $\color{red}{136m}$ $\color{green}{\text{in a 1000m or 1km race}}$