Two cars starts from Ahmadabad and run in opposite direction with one car's speed being 200 km/h more than the other. If they are 4500 km apart after 9 h, then the sum of the speeds of both the cars is:

Correct option is A

Given:

Speed of  one car is 200 km/h more than the other car.

Distance travelled = 45000 km

Time taken = 9 h

Formula used:

Speed = $$\frac{Distance}{Time}$$

Solution:

Let speed of car A = $$x$$  km/h

Speed of car B = $$(x + 200)$$ km/h

Now, according to question:

​$$\begin{aligned}4500 &= (x) \times 9 + (200 + x) \times 9 \\&\Rightarrow 500 = x + 200 + x \\&\Rightarrow 2x = 300 \\&\Rightarrow x = 150 \quad \text{and} \quad (200 + x) = 350 \\\end{aligned}$$ 

Sum of Speed of A and B = 150 +350 = 500 km/h

Alternate Solution:

Relative Speed of A and B (in opposite direction) = $$2x+200$$ 

Now according to question:

  $$4500 = (2x+200) \times 9\\2x + 200 = 500\\2x = 300\\x = 150$$ 

Therefore, Speed of A = 150 km/h

Speed of B =  150 + 200 = 350 km/h 

Total Speed of both the cars = 500 km/h