Question : A bus starts running with an initial speed of 21 km/hr, and its speed increases by 3 km/hr every hour. How many hours will it take to cover a distance of 252 kilometres?
Option 1: 3
Option 2: 5
Option 3: 8
Option 4: 10
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Correct Answer: 8
Solution :
Given: Initial speed ($a$) = 21 km/hr
Increase in speed every hour ($d$) = 3 km/hr
This is an arithmetic progression, with the initial number ($a$) = 21 and the common difference ($d$) = 3
Also, the sum of A.P. = $\frac{n}{2}[2a + (n - 1)d]$
⇒ 252 = $\frac{n}{2}[2×21+(n-1)3]$
⇒ $3n^2+ 39n - 504 = 0$
⇒ $n^2+13n-168=0$
⇒ $(n – 8)(n + 21)=0$
⇒ $n = 8, –21$
Since the number of hours can’t be negative, the time taken is 8 hours.
Hence, the correct answer is 8.
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