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

• A. 29
• B. 27
• C. 28
• D. 26

Answer 1

The Correct Option is C

The correct answer is (C): \(28\)
Let the original time taken by Vimla be \(t\) minutes \(\frac{40t}{60} = \frac{35×(t+6)}{60}\)

\(⇒ t=35×\frac{6}{5}=42\) \(min\)

The distance to office = \(28\) \(km\) 

Required answer = \(\frac{28×\frac{1}{3}}{42×\frac{2}{3}-8}×60 = 28\) \(kmph\)

Answer 2

So, we obtain the distance as:
40t = 35 × [t + (6/60)]
⇒ 5t = 7/2
⇒ t = 42 minutes
So, the total distance = 40 × (42/60) = 28 km
⅓ of her usual time = 42/3 = 14 minutes
Remaining distance = 28/3 km
Let the required speed be v km/h
⇒ (14/60) + (8/60) + (28/3v) = 42/60

∴ v = 28 km/h