Question

Sita was running on a circular track of length 500 metres. She completed her first round in 3 min. In her second round she took a detour which increased
the distance she ran by 10%, but she ran faster and took 10% less time than the first round. What was her speed in the second round?
Pick ONE option
A) 12.22 km/hr.
B) 13.5 km/hr
C) 11 km/hr
D; 11.67 km/hr
​

Answer 1

First, Let's look into the first round.

She ran a distance of 500 m and took only 3 minutes to complete the round.

Now, In the second round, She took a detour ( long route ) which increased the distance by 10% but she ran faster and took 10% less time than the first round.

⇒ Distance travelled = 500 + 10% of 500

⇒ Distance = 500 + 10/100 × 500

⇒ Distance = 500 + 50

⇒ Distance = 550 m

Also,

⇒ Time taken = 180s - 10% of 180 s

[ ∵ 1 minute = 60 s ]

⇒ Time taken = 180 - 10/100 × 180

⇒ Time taken = 180 - 18

⇒ Time taken = 162 s

Now that we are given the speed in km/hr in the options, so we would have to find it in km/hr

First, Convert distance into km and time into hr

⇒ Distance = 550/1000 [ 1 km = 1000 m ]

⇒ Distance = 0.55 km

Similarly,

⇒ Time taken = 162 /3600 [ 1 hour = 3600 s ]

⇒ Time taken = 0.045 hour

Now,

⇒ Speed = Distance / Time

⇒ Speed = 0.55 / 0.045

⇒ Speed = 12.22... km/hr

Or, Speed ≈ 12.22 km/hr

Hence, Speed in the second round was 12.22 km/hr.

∴ Option (A) is correct.