In a 100m race, A beats B by 10m and B beats C by 10m. By what distance does A beat C (in m)?

In a 100m race, A beats B by 10m.

Let's assume the distance covered by A is 100m.

The distance covered by B = 100-10 = 90m

So here both A and B are taking the same time which can be assumed as 'Y'.

Speed of A = $$\frac{100}{Y}$$    Eq.(i)

Speed of B = $$\frac{90}{Y}$$     Eq.(ii)

B beats C by 10m.

Let's assume the distance covered by B is 100m.

The distance covered by C = 100-10 = 90m

So here both B and C are taking the same time which can be assumed as 'Z'.

Speed of B = $$\frac{100}{Z}$$    Eq.(iii)

Speed of C = $$\frac{90}{Z}$$    Eq.(iv)

Eq.(ii) = Eq.(iii)

$$\frac{90}{Y} = \frac{100}{Z}$$

$$Y=\frac{9}{10}Z$$

Put the value of 'Y' in Eq.(i).

Speed of A = $$\frac{1000}{9Z}$$    Eq.(v)

As we know that when time constant, then the speed is directly proportion to the disatnce.

Eq.(v) : Eq.(vi)

$$\frac{1000}{9Z}$$ : $$\frac{90}{Z}$$

$$\frac{1000}{9}$$ : $$\frac{90\times9}{9}$$

$$\frac{1000}{9}$$ : $$\frac{810}{9}$$

100 : 81

So A beat C by (100-81) = 19 m