DIRECTIONS for the question: Solve the following question.Road A and road B are two concentric circular roads. A man starts running at 12 km/hr from a point P on the outer road B along a path tangential to road A and takes 50 minutes to reach point Q on road B. If the radii of the two roads are integers, what is the diameter of road B? (ans in km, in numerical value)Correct answer is '26'. Can you explain this answer?

Question

Answer

Problem Analysis:
To solve this problem, we need to find the diameter of road B. Given that the man starts running from point P on road B and reaches point Q on the same road, we can infer that the path between P and Q is a straight line. This straight line is tangential to road A.

We are also given the speed of the man, which is 12 km/hr, and the time taken to reach point Q, which is 50 minutes.

To solve this problem, we can use the formula:

Distance = Speed × Time

Solution:
Let's solve the problem step by step.

Step 1: Convert the time from minutes to hours.
Given that the time taken is 50 minutes, we need to convert it to hours.
50 minutes = 50/60 hours = 5/6 hours

Step 2: Calculate the distance traveled by the man.
Distance = Speed × Time
Distance = 12 km/hr × 5/6 hr
Distance = 10 km

Step 3: Calculate the radius of road B.
Since the man starts from point P on road B and reaches point Q on road B, the distance traveled by the man is equal to the circumference of road B.
Distance = Circumference of road B
10 km = 2πr
r = 10 km / (2π)
r ≈ 1.59 km

Step 4: Calculate the diameter of road B.
Diameter = 2 × radius
Diameter = 2 × 1.59 km
Diameter ≈ 3.18 km

Step 5: Check for the given condition that the radii of the two roads are integers.
Since the diameter of road B is not an integer, we need to find another value for the diameter.

Step 6: Calculate the distance traveled by the man again.
Since the radius of road B is an integer, let's assume it to be 2 km.
Distance = Circumference of road B
Distance = 2πr
Distance = 2π(2 km)
Distance ≈ 12.57 km

Step 7: Calculate the time taken by the man.
Time = Distance / Speed
Time ≈ 12.57 km / 12 km/hr
Time ≈ 1.048 hours

Step 8: Convert the time to minutes.
Time = 1.048 hours × 60 minutes/hour
Time ≈ 62.88 minutes

Step 9: Check if the calculated time matches the given time.
Since the calculated time is not equal to 50 minutes, the assumed radius of 2 km is incorrect.

Step 10: Calculate the distance traveled by the man again.
Since the radius of road B is an integer, let's assume it to be 13 km.
Distance = Circumference of road B
Distance = 2πr
Distance = 2π(13 km)
Distance ≈ 81.64 km

Step 11: Calculate the time taken by the man.
Time = Distance / Speed
Time ≈ 81.64 km / 12 km/hr
Time

Similar CAT Doubts

DIRECTIONS for the question: Solve the following question.Consider the set X = {1, 2, 3, ..., 9, 10}. A and B are two non-empty disjoint subsets of X such that A ∪ B = X. The products of all the elements in A and B are represented by prod(

DIRECTIONSfor the question:Solve the following question and write the answer (in numerical valu e).A person gives 40% discount and still makes a profit of 20%. If he gives a discount of 25% only, what is his profit percentage? Correct answer is '50'. Can you explain this answer?

Top Courses for CATView all

Quantitative Aptitude (Quant)

Crash Course for CAT

CAT Mock Test Series 2024

3 Months Preparation for CAT

CAT Mock Test Series and 500+ Practice Tests 2024

Top Courses for CAT

Top Courses for CAT

Suggested Free Tests

Related Content

About CAT

CAT Preparation Material

How to Prepare for CAT Exam?

CAT Mock Tests

Other MBA Exams

Other Popular Exams

Company