Question:medium

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

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

Solution and Explanation

Step 1: Define Total Distance

Let the total distance to the office be \( d \) km.

Step 2: Calculate Usual Travel Time

Vimla's usual speed is 40 km/hr. Her usual time to reach the office is \( \frac{d}{40} \) hours.

Step 3: Formulate Equation for Late Arrival

When traveling at 35 km/hr, she is 6 minutes late. 6 minutes is \( \frac{1}{10} \) hour. The equation is: \( \frac{d}{35} = \frac{d}{40} + \frac{1}{10} \)

Step 4: Solve for Distance

Solving the equation: \( \frac{d}{35} - \frac{d}{40} = \frac{1}{10} \Rightarrow \frac{40d - 35d}{1400} = \frac{1}{10} \Rightarrow \frac{5d}{1400} = \frac{1}{10} \Rightarrow d = 28 \) km.

Step 5: Determine Usual Travel Time in Minutes

The usual travel time is \( \frac{28}{40} = 0.7 \) hours, which is 42 minutes.

Step 6: Calculate Distance Covered in One-Third of Time

One-third of 42 minutes is 14 minutes. The distance covered in this time at her usual speed is \( \frac{2}{3} \times 28 \approx 18.67 \) km. (Note: The input implies this calculation is done using the total distance, not speed in the first 14 minutes, which is inconsistent. Assuming the intention is to find the distance covered in the first portion of the journey if it were to be one-third of the usual time). Alternatively, if the question implies she drove for 14 minutes at 40 km/hr: \( 40 \times \frac{14}{60} = \frac{40 \times 14}{60} = \frac{560}{60} \approx 9.33 \) km.

Step 7: Calculate Remaining Time After Stop

After covering a portion of the distance and stopping for 8 minutes, the remaining time to reach the office is \( 42 - 14 - 8 = 20 \) minutes, which is \( \frac{1}{3} \) hour.

Step 8: Calculate Remaining Distance

The remaining distance to be covered is \( 28 - 18.67 = 9.33 \) km.

Step 9: Calculate Required Speed for Remaining Distance

The required speed to cover 9.33 km in 20 minutes (\( \frac{1}{3} \) hour) is \( \text{Speed} = \frac{9.33}{\frac{1}{3}} = 9.33 \times 3 = 28 \) km/hr.

Final Answer:

Vimla should drive the remaining distance at a speed of \( \boxed{28 \text{ km/hr}} \).

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