Multiple choice

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

  1. 29

  2. 27

  3. 28

  4. 26
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Usual time = D/40. Late by 6 min (0.1 hr) at 35 km/hr: D/35 - D/40 = 0.1. D/280 = 0.1, D = 28 km. Usual time = 28/40 = 0.7 hr (42 min). One day: 2/3 distance (18.66 km) in 1/3 time (14 min). Remaining distance = 9.33 km. Remaining time = 42 - 14 - 8 = 20 min (1/3 hr). Speed = 9.33 / (1/3) = 28 km/hr.

AI explanation

Let the usual distance be D km, so the usual time taken is D/40 hours. Using the difference in times equation, D/35 - D/40 = 6/60, which gives D/280 = 1/10 and a usual distance of 28 km. The usual time is 28/40 hours, so one-thirds of this usual time is (1/3)*(7/10) = 7/30 hours, during which she covers two-thirds of the distance, or 56/3 km. She stops for 8 minutes (which is 2/15 hours), and she started at 9 am with a total usual time of 42 minutes, meaning she has 42 - 14 - 8 = 20 minutes left to cover the remaining one-third distance of 28/3 km. Using the formula Speed equals Distance divided by Time, the required speed is (28/3) divided by (20/60), which calculates to 28 km/hr. The result is 28.

Keep practicing — related questions