The speed of a car increases by 2 km/h after every hour. If it travels 35 km in the first hour, what is the total distance travelled by the car in 12 hours?

Introduction / Context:
This question belongs to the time and distance chapter and involves an arithmetic progression in speeds. The car does not move at a uniform speed; instead, its speed increases by a fixed amount every hour. You must recognise that the distance covered in each hour forms an arithmetic series because distance in each hour equals speed in that hour for a duration of one hour.

Given Data / Assumptions:

• Distance covered in the first hour = 35 km, so speed in first hour = 35 km/h.
• Speed increases by 2 km/h after every hour.
• Total duration of travel = 12 hours.
• We assume the change in speed happens at the end of each full hour.

Concept / Approach:
For each hour, distance = speed * time. Time each hour is 1 hour. Hence distances in successive hours are equal to the speeds: 35, 37, 39, and so on, forming an arithmetic progression with first term a = 35, common difference d = 2, and number of terms n = 12. Total distance is the sum of this arithmetic series:
Sum = n / 2 * [2a + (n - 1) * d].

Step-by-Step Solution:
Step 1: First hour speed a = 35 km/h. Step 2: Common difference d = 2 km/h. Step 3: Number of hours n = 12, so there are 12 terms in the series. Step 4: Use formula: Sum = n / 2 * [2a + (n - 1) * d]. Step 5: Sum = 12 / 2 * [2 * 35 + (12 - 1) * 2] = 6 * [70 + 22] = 6 * 92 = 552 km.
Verification / Alternative check:
We can manually list the speeds for a quick check: 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57. Pairing first and last terms: 35 + 57 = 92. There are 6 such pairs, so total distance = 6 * 92 = 552 km. This matches the formula based calculation and confirms the answer.

Why Other Options Are Wrong:

• 456 km: Too low; it corresponds to using fewer terms or a smaller common difference.
• 482 km: Also lower; may come from miscounting number of hours or misusing the formula.
• 556 km: Slightly higher, indicating a numerical mistake when adding terms.

Common Pitfalls:

• Assuming constant speed and multiplying 35 by 12, which ignores the increasing pattern.
• Using n instead of n - 1 inside the bracket of the arithmetic series formula.
• Forgetting that each term represents distance for exactly one hour of travel.

Final Answer:
The total distance travelled by the car in 12 hours is 552 km.