SSC Selection Post 2023 PYQ — Question 64

The correct answer is Option 4 i.e.15 hours.

Let speed of X = x km/hr

Then speed of Y = x − 40 km/h

Time taken by X = $1200\over x$

Time taken by Y = $1200\over x-40$

According to the question,

⇒ $1200\over x-40$ - $1200\over x$ = 5

⇒ $1200(x-x+40)\over x(x-40)$ = 5

⇒ 1200 × 40 = 5x² - 200x

⇒ x² - 40x - 9600 = 0

⇒ x² - 120x + 80x - 9600 = 0

⇒ (x - 120)(x + 80) = 0

⇒ x = 120, -80

So, speed of X = 120 km/h

Speed of Y = 80 km/h

Time taken by Y = $1200\over80$ = 15 hours