Q. 22: 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
Vimala’s speed has decreased from 40kmph to 35 kmph. That means her current speed is 35/40 of the original Speed. That means, her current speed is 7/8 th of the original speed. Therefore, the time taken will be 8/7 th of the original time taken.
Since she is 6 minutes late when travelling at 35kmph, 1/7th of the original time taken is 6 minutes.
Therefore the total time taken originally is 7 × 6 = 42 minutes.
1/3 rd of the original time taken = 42/3 = 14 minutes.
1/3 rd of the total distance is generally covered in 14 minutes.
Currently the same distance is to be covered in (42 – 14 – 8 = 20) minutes.
So, to reach the Destination on time, Vimala, must cover the same 1/3 rd of the Distance in 20 minutes instead of 14 minutes.
That means she has to 20/14 of the initial time.
Which is 10/7 of the original time
This implies that, in order to reach at the same point of time. The speed had to 7/10 or 70% of the original speed.
So, she has to travel at 70% of 40kmph = 28kmph.