Q. Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A. If the distance between A and B is 50 km, what is the speed of the slower rabbit?
1) 20 km/h
2) 10 km/h
3) 15 km/h
4) 25 km/h
Answers
Answer:
1) 20 km/h
Explanation:
HomeQuantitative AptitudeSpeed Time and DistanceRelative Speed
Question
Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A. If the distance between A and B is 50 km, what is the speed of the slower rabbit?
This question was previously asked in
IB ACIO Grade II Previous Paper 1 (Held On: 15 Oct 2017
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20 km/h
10 km/h
15 km/h
25 km/h
Answer (Detailed Solution Below)
Option 1 : 20 km/h
Detailed Solution
Given:
Two rabbits start running towards each other, one form A to B and another from B to A.
They cross each other after one hour and the first rabbit reaches B, 5/6 hour before the second rabbit reaches A
Distance between A and B = 50 km
Formula:
Speed = distance/time
Calculation:
Let the speed of slower rabbit and faster rabbit be x km/hr and y km/hr respectively.
According to the question
x + y = 50/1
⇒ x + y = 50 --- (1)
Again,
50/x – 50/y = 5/6 --- (2)
From (1) and (2), we get
50/x – 50/(50 – x) = 5/6
⇒ 60 (50 – x – x) = x (50 – x)
⇒ 3000 – 120x = 50x – x2
⇒ x2 – 170x + 3000 = 0
⇒ (x – 150) (x – 20) = 0
⇒ x = 20 (∵ x = 150 not possible)