A person reaches his destination 30 minutes late if his speed is 3 km/h, and reaches 30 minutes before time if his speed is 4 km/h. Find the distance of his destination from his starting point.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12 km.
Given,
A person reaches his destination 30 minutes late if his speed is 3 km/h, and reaches 30 minutes before time if his speed is 4 km/h
According to the question;
Let the distance between the starting point and the destination be d km.
Let the normal time taken to reach the destination be t hours.
When the person is traveling at 3 km/h, he reaches 30 mins late,
⇒ d/3 = t + 30/60
⇒ t = d/3 - 1/2 ----- (1)
When the person is traveling at 4 km/h, he reaches 30 mins early,
⇒ d/4 = t - 30/60
⇒ t = d/4 + 1/2 ----- (2)
Now, equation (1) = equation (2),
⇒ d/3 - 1/2 = d/4 + 1/2
⇒ d/3 - d/4 = 1/2 + 1/2
⇒ (4d - 3d)/12 = 1
⇒ d = 12 km