In a race A, B and C take part A beats B by 30 meters, B beats C by 20 meters and A beats C by 48 meters.
Given below are two statements:
Statement I : The length of the race is 300 meters.
Statement II : The speed of A, B and C are in the ratio 50 : 45 : 40.
In the light of the above statements, choose the correct answer from the options given below:

Let say length of race be $$D$$ metres and speed of $$A$$, $$B$$ and $$C$$ be $$S_A,\ S_B,\ S_c$$ m/s.

Now, A beats B by 30 meters

So, $$\dfrac{S_A}{S_B}=\dfrac{D}{D-30}$$ --->(1)

Also, B beats C by 20 meters

So, $$\dfrac{S_B}{S_C}=\dfrac{D}{D-20}$$ ----->(2)

Also, A beats C by 48 meters.

So, $$\dfrac{S_A}{S_C}=\dfrac{D}{D-48}$$ ---->(3)

Multiplying (1) and (2) and equating with option (3),

$$\dfrac{D}{D-30}\times\ \dfrac{D}{D-20}=\dfrac{D}{D-48}$$

or, $$D\left(D-48\right)=\left(D-30\right)\left(D-20\right)$$

or, $$D^2-48D=D^2-50D+600$$

or, $$50D-48D=600$$

or, $$2D=600$$

or, $$D=300$$ meters

Putting the value of $$D$$ in (1) and (2),

$$\dfrac{S_A}{S_B}=\dfrac{300}{300-30}=\dfrac{300}{270}=\dfrac{10}{9}=\dfrac{50}{45}$$

$$\dfrac{S_B}{S_C}=\dfrac{300}{280}=\dfrac{15}{14}=\dfrac{45}{42}$$

The speed of A, B and C are in the ratio 50 : 45 : 42.

So, the correct answer is option C, statement I is true but statement II is false.