Question:medium

A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in first hour was 30 km, is

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When speed (or distance per hour) increases by a fixed amount each hour, use the sum of an AP: $S_n=\frac{n}{2}[2a+(n-1)d]$.
Updated On: Jul 15, 2026
  • 266 km
  • 273 km
  • 280 km
  • 287 km
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The Correct Option is B

Approach Solution - 1

Step 1: The hourly distances form an arithmetic sequence starting at 30 km with common difference 3 km, so the seventh hour's distance is \( 30+6 \times 3=48 \) km.

Step 2: The sum of an arithmetic sequence equals the number of terms times the average of the first and last terms. Here the average of 30 km and 48 km is \( \frac{30+48}{2}=39 \) km.

Step 3: The total distance over 7 hours is \( 7 \times 39=273 \) km.
\[ \boxed{273 \text{ km}} \]
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Approach Solution -2

Pair up the seven hourly distances from the two ends inward: the first and seventh, the second and sixth, the third and fifth, leaving the fourth hour by itself in the middle. Each such pair adds up to the same total, since the amounts gained on one side match the amounts lost on the other. We can check each option against the sum built this way.

  1. 266 km: Pairing gives \( (30+48)+(33+45)+(36+42)+39=78+78+78+39=273 \) km, not 266.
  2. 273 km: The paired sum \( 78+78+78+39=273 \) km matches this exactly.
  3. 280 km: This does not match the paired sum of 273 km.
  4. 287 km: This does not match the paired sum of 273 km either.

Pairing the hourly distances from both ends confirms three equal pairs of 78 km each plus the unpaired middle hour of 39 km, totalling 273 km.

Therefore, the correct answer is 273 km.

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