Question:medium

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

Updated On: Jan 15, 2026
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The Correct Option is B

Solution and Explanation

Provided:

  • Standard speed = \( s \)
  • Standard time = \( t \)
  • Speed reduced to \( \frac{s}{3} \), resulting in a 30-minute (\( \frac{1}{2} \) hour) delay.

Step 1: Total Distance

Total distance = \( s \cdot t \)

Step 2: Time lost due to reduced speed

Initial speed is \( \frac{s}{3} \). Assuming time for this segment is 5 minutes (\( \frac{1}{12} \) hour).

Distance covered in this time: \( \frac{s}{3} \cdot \frac{1}{12} = \frac{s}{36} \)

Step 3: Remaining Distance and Required Speed

Assuming standard time is 1 hour, remaining time is \( \frac{11}{12} \) hour.

To compensate for the delay, the required speed \( v \) must cover the remaining distance:

\[ v = \frac{\text{Remaining distance}}{\text{Time left}} = \frac{s \cdot t - \frac{s}{36}}{t - \frac{1}{12}} \]

Alternatively, using the proportion method:

The last \( \frac{2st}{3} \) distance must be covered in \( \frac{2t}{5} \) time (6 minutes).

Required speed: \[ = \frac{\frac{2st}{3}}{\frac{2t}{5}} = \frac{5s}{3} \]

Step 4: Calculate % Increase in Speed

\[ \text{Increase} = \frac{\frac{5s}{3} - s}{s} \cdot 100 = \frac{2s}{3s} \cdot 100 = \frac{2}{3} \cdot 100 = 66.\overline{6}\% \]

Final Answer: 67%

Correct Option: (B)

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The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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