A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr. Then his original speed isa)25 km/hrb)20 km/hrc)26 km /hrd)24 km/hrCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Distance = 200 km
Let the original speed of the cyclist be x km/hr

To Find:
The original speed of the cyclist

Solution:
Case 1: When the cyclist travels at the original speed of x km/hr

Time taken to cover the distance of 200 km = Distance/Speed
= 200/x hours

Case 2: When the cyclist increases his speed by 5 km/hr

New speed = x + 5 km/hr

Time taken to cover the same distance of 200 km = Distance/Speed
= 200/(x+5) hours

According to the question, the time taken in Case 2 is 2 hours less than the time taken in Case 1.

So, we can write the equation as:

200/x - 200/(x+5) = 2

Multiplying both sides by x(x+5), we get:

200(x+5) - 200x = 2x(x+5)

Simplifying the above equation, we get:

1000 = 2x^2 + 10x

2x^2 + 10x - 1000 = 0

x^2 + 5x - 500 = 0

Solving the above quadratic equation, we get:

x = (-5 + sqrt(25 + 2000))/2 OR x = (-5 - sqrt(25 + 2000))/2

x = (-5 + 45)/2 OR x = (-5 - 45)/2

x = 20 OR x = -25

Since the speed cannot be negative, the original speed of the cyclist is 20 km/hr.

Therefore, the correct option is (B) 20 km/hr.

Similar Quant Doubts

Ajay covers certain distance with his own speed but when he reduces his speed by 10kmph his time duration for the journey increases by 40 hours while if he increases his speed by 5 kmphfrom his original speed he takes 10 hours less than the original time taken. Find the distance covered by him.

A jeep travels a distance of 100 km at a uniform speed. If the speed of the jeep is 5 kmph more, then it takes 1 hour less to cover the same distance. The original speed of the jeep is

A person covers a certain distance at a he es 1 increases his speed by 25% then he take minutes less to cover the same distance. Find the time He by him initially to cover the distance at the original speed Correct answer is '7'. Can you explain this answer?

In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?

Sohail covers a distance by walking for 6 hours. While returning, his speed decreases by 2kmph and he takes 9 hours to cover the same distance. What was his speed while returning?

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company