Subject: General Aptitude · Chapter: Time and Distance · Exam: 2007 · Marks: · Difficulty:
A car starts running with the initial speed of 40 kmph, with its speed increasing every hour by 5 kmph. How many hours will it take to cover a distance of 385 km?
(a)7 hours
(b)$8 \frac{1}{2}$ hours
(c)9 hours
(d)$9 \frac{1}{2}$ hours
Answer
Answer (as printed): A
Explanation
Let the required number of hours be $n$. Clearly, the car covers 40 km in the first hour, 45 km in the second hour, 50 km in the third hour, and so on. Thus, $40+45+50+\ldots$ upto $n$ terms $=385$. This is an A.P. with first term $a=40$, common difference $d=5$. $$\therefore S_n=\frac{n}{2}[2 \times 40+(n-1) 5]$$ So, $\frac{n}{2}[80+5(n-1)]=385 \Leftrightarrow 80n+5n^2-5n=770$ $$\Leftrightarrow 5n^2+75n-770=0 \Leftrightarrow n^2+15n-154=0$$ $$\Leftrightarrow n^2+22n-7n-154=0 \Leftrightarrow n(n+22)-7(n+22)=0$$ $$\Leftrightarrow (n+22)(n-7)=0 \Leftrightarrow n=7.$$ Hence, required number of hours $=7$.
Explanation as extracted from the printed page; notation may be imperfect.