SSC CPO 2023 PYQ — Question 134

The correct answer is Option 4 i.e 40.

Let the speed of a fast train be x km/hr

Speed of slower train = x - 10 km/hr

Given fast train takes 1 hour less than a slower one to cover 200 km

⇒ ${200\over x }= {200\over (x - 10)} - 1$

⇒ $\frac{200}{x} = \frac{200 - (x - 10)} {(x - 10)}$

⇒ 200(x - 10) = 200x - x(x - 10)

⇒ 200x - 2000 = 200x - x² + 10x

⇒ x² - 10x - 2000 = 0

⇒ x² - 50x + 40x - 2000 = 0

⇒ (x - 50)(x + 40) = 0

x = 50 and x = - 40     (x can't be negative)

So x= speed of faster train = 50 km/hr

Speed of slower train = 40 km/hr