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

Updated On: Jul 15, 2026
  • 266 km
  • 273 km
  • 280 km
  • 287 km
Show Solution

The Correct Option is B

Approach Solution - 1

Step 1: Understanding the Question.
The car's speed rises by 3 km/hr every hour, and the distance covered in the first hour is 30 km. We need the total distance covered over 7 hours.

Step 2: Key Formula or Approach.
Since the distance covered each hour goes up by a fixed 3 km each time, the 7 hourly distances form an arithmetic sequence with first term \( a = 30 \) and common difference \( d = 3 \). We add up all 7 terms directly.

Step 3: Detailed Explanation.
The distance covered in each of the 7 hours is:
\[ 30, \ 33, \ 36, \ 39, \ 42, \ 45, \ 48 \]
Adding these one by one:
\[ 30 + 33 = 63 \]
\[ 63 + 36 = 99 \]
\[ 99 + 39 = 138 \]
\[ 138 + 42 = 180 \]
\[ 180 + 45 = 225 \]
\[ 225 + 48 = 273 \]

Step 4: Final Answer.
The total distance travelled in 7 hours is 273 km. \[ \boxed{273 \text{ km}} \]
Was this answer helpful?
0
Show Solution

Approach Solution -2

Another way to sum this sequence is by pairing terms from opposite ends, a technique that works because the sequence increases by a constant amount. The 7 hourly distances are 30, 33, 36, 39, 42, 45, 48 km. Pairing the 1st and 7th terms, the 2nd and 6th, and the 3rd and 5th: \( 30 + 48 = 78 \), \( 33 + 45 = 78 \), and \( 36 + 42 = 78 \), each pair adding to the same value since the terms are equally spaced. This leaves the 4th term, 39, unpaired in the middle. The total distance is therefore \( 3 \times 78 + 39 = 234 + 39 = 273 \) km. Let's check each option against this fixed pairing sum.

  1. Option (A): 266 km: This is 7 km less than the pairing total of 273 km, meaning it does not match the invariant pair-sum of 78 repeated three times plus the middle term of 39.
  2. Option (B): 273 km: This matches \( 3 \times 78 + 39 = 273 \) exactly, obtained from pairing the extreme terms of the sequence.
  3. Option (C): 280 km: This is 7 km more than the pairing total, so it does not correspond to the actual sequence of distances 30 through 48.
  4. Option (D): 287 km: This is 14 km more than the pairing total, an even larger mismatch with the actual sequence.

Pairing the equally-spaced hourly distances from both ends consistently gives a total of 273 km.

Therefore, the correct answer is 273 km.

Was this answer helpful?
0

Top Questions on Ratio and Proportion

Questions Asked in CLAT exam

Read the passage and answer the question.

Passage (extract): The work which Gandhiji had taken up was not only regarding the achievement of political freedom but also the establishment of a new social order based on truth and non-violence, unity and peace, equality and universal brotherhood and maximum freedom for all. A new order cannot be established without radically changing the mind and attitude of men towards property and, at some stage or the other, the 'haves' have to yield place to the 'have-nots'. We have seen, in our time, attempts to achieve a kind of egalitarian society and the picture of it after it was achieved. But this was done, by and large, through the use of physical force. It may even be that, like a gas kept confined within containers under great pressure, or water held back by a big dam, once the barrier breaks, the reaction will one day sweep back with a violence equal in extent and intensity to what was used to establish and maintain the outward egalitarian form. This enforced egalitarianism contains, in its bosom, the seed of its own destruction. If egalitarianism is to endure, it has to be based not on the possession of the maximum material goods by a few or by all but on voluntary, enlightened renunciation of those goods which cannot be shared by others or can be enjoyed only at the expense of others.

According to the passage, egalitarianism will not survive if
View Solution
Read the passage and answer the question.

Passage (extract): The work which Gandhiji had taken up was not only regarding the achievement of political freedom but also the establishment of a new social order based on truth and non-violence, unity and peace, equality and universal brotherhood and maximum freedom for all. This unfinished part of his experiment was perhaps even more difficult to achieve than the achievement of political freedom. In the political struggle, the fight was against a foreign power and all one could do was either join it or wish it success and give it his/her moral support. In establishing a social order on this pattern, there was a strong possibility of a conflict arising between diverse groups and classes of our own people.

According to the passage, which was the unfinished part of Gandhi's experiment?
View Solution
Read the passage and answer the question.

Passage (extract): In the political struggle, the fight was against a foreign power and all one could do was either join it or wish it success and give it his/her moral support. Experience shows that man values his possessions even more than his life because in the former he sees the means for perpetuation and survival of his descendants even after his body is reduced to ashes. We have seen, in our time, attempts to achieve a kind of egalitarian society and the picture of it after it was achieved. But this was done, by and large, through the use of physical force. This enforced egalitarianism contains, in its bosom, the seed of its own destruction. The root cause of class conflict is possessiveness or the acquisitive instinct.

Which of the following statements is 'not true' in the context of the passage?
View Solution