Question:
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
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
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
The correct option is (B): 273 km.
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Approach Solution -2
The driver's speed goes up by 3 km/hr every hour, and he covers 30 km in the first hour, so the distance covered each hour forms a sequence increasing by 3 km/hr. The total distance over 7 hours is the sum of this sequence, which we can check against each option using the average-times-terms method.
- Option (A): 266 km: Dividing 266 by 7 hours gives an average hourly distance of 38 km, but the actual average of the sequence 30, 33, 36, 39, 42, 45, 48 is 39 km, so 266 is too low.
- Option (B): 273 km: Dividing 273 by 7 gives an average of exactly 39 km per hour. For an evenly increasing sequence, the average equals the middle (4th) term, which is 30 + 3(3) = 39 km, exactly matching.
- Option (C): 280 km: This gives an average of 40 km per hour, one more than the actual middle term of 39 km, so this overshoots the correct total.
- Option (D): 287 km: This gives an average of 41 km per hour, which is too high compared to the required average of 39 km.
Since the sequence of hourly distances is evenly spaced, its average equals the 4th (middle) term, 39 km, and 7 hours at that average gives 273 km.
Therefore, the correct answer is 273 km.
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Approach Solution -3
The distances covered each hour form an arithmetic sequence with first term \( a = 30 \) km and common difference \( d = 3 \) km, since the speed rises by 3 km/hr every hour. Using the sum formula for an arithmetic series, \( S_n = \frac{n}{2} \left[ 2a + (n - 1)d \right] \), with \( n = 7 \): \[ S_7 = \frac{7}{2} \left[ 2(30) + (6)(3) \right] = \frac{7}{2} \left[ 60 + 18 \right] = \frac{7}{2} \times 78 = 273 \] Let's check each option by working out what common difference it would actually require, keeping \( a = 30 \) and \( n = 7 \) fixed.
- Option (A): 266 km: Solving \( 266 = \frac{7}{2} \left[ 60 + 6d \right] \) gives \( 6d = \frac{2 \times 266}{7} - 60 = 76 - 60 = 16 \), so \( d \approx 2.67 \) km/hr, not the given 3 km/hr increase, so this total does not fit.
- Option (B): 273 km: This matches \( S_7 = \frac{7}{2}\left[60 + 18\right] = 273 \) exactly, using the given \( a = 30 \) and \( d = 3 \).
- Option (C): 280 km: Solving \( 280 = \frac{7}{2}\left[60 + 6d\right] \) gives \( 6d = 80 - 60 = 20 \), so \( d \approx 3.33 \) km/hr, which does not match the stated 3 km/hr increase.
- Option (D): 287 km: Solving \( 287 = \frac{7}{2}\left[60 + 6d\right] \) gives \( 6d = 82 - 60 = 22 \), so \( d \approx 3.67 \) km/hr, again inconsistent with the given rate of increase.
Only a common difference of exactly 3 km/hr, as stated in the question, produces a total distance of 273 km through the arithmetic series sum formula.
Therefore, the correct answer is 273 km.
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