Question:

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: Jul 25, 2025

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The Correct Option is C

Approach Solution - 1

Step 1: Let the total distance to the office be

\[ d \text{ km} \]

Step 2: Usual speed and time

Vimla's usual speed is 40 km/hr. So her usual time to reach the office: \[ = \frac{d}{40} \text{ hours} \]

Step 3: Late by 6 minutes when going at 35 km/hr

6 minutes = \( \frac{1}{10} \) hour. So the equation becomes: \[ \frac{d}{35} = \frac{d}{40} + \frac{1}{10} \]

Step 4: Solve the equation

\[ \frac{d}{35} - \frac{d}{40} = \frac{1}{10} \Rightarrow \frac{40d - 35d}{1400} = \frac{1}{10} \Rightarrow \frac{5d}{1400} = \frac{1}{10} \Rightarrow d = 28 \text{ km} \]

Step 5: Usual travel time

\[ \frac{28}{40} = 0.7 \text{ hours} = 42 \text{ minutes} \]

Step 6: One-third of time and distance covered

One-third of 42 minutes = 14 minutes. Distance covered in that time: \[ \frac{2}{3} \times 28 = 18.67 \text{ km} \]

Step 7: Time left after stopping

Stop time = 8 minutes Remaining time to reach office: \[ 42 - 14 - 8 = 20 \text{ minutes} = \frac{1}{3} \text{ hour} \]

Step 8: Remaining distance to be covered

\[ 28 - 18.67 = 9.33 \text{ km} \]

Step 9: Required speed to cover 9.33 km in 20 minutes

\[ \text{Speed} = \frac{9.33}{\frac{1}{3}} = 9.33 \times 3 = \boxed{28 \text{ km/hr}} \]

Final Answer:

Vimla should drive the remaining distance at a speed of \[ \boxed{28 \text{ km/hr}} \]

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