A bus starts running with the initial speed of 21 km/hr and its speed increases every hour by 3 km/hr. How many hours will it take to cover a distance of 252 km?

Initial speed of bus = 21 km/hr

Speed of bus after each hour = 21,24,27,30,.... km/hr

This is clearly an AP with sum = $$\frac{n}{2}[2a+(n-1)d]$$

Let time taken = $$n$$ hours

=> $$\frac{n}{2}[2(21)+(n-1)3]=252$$

=> $$n(39+3n)=504$$

=> $$3n^2+39n-504=0$$

=> $$n^2+13n-168=0$$

=> $$n^2+21n-8n-168=0$$

=> $$n(n+21)-8(n+21)=0$$

=> $$(n-8)(n+21)=0$$

=> $$n=8,-21$$

$$\because n$$ can't be negative, => Time taken = 8 hours

=> Ans - (C)