Question

Ajay walks at a speed of 4 km/hr. He doubles his speed after reaching exactly halfway. He walks for 12 hours in all. What is the total distance travelled by him?

• A. 32 km
• B. 30 km
• C. 60 km
• D. 64 km

Answer 1

The Correct Option is D

Ajay's walking journey is divided into two parts: The first half where he walks at 4 km/hr and the second half where he doubles his speed to 8 km/hr. He walks for a total of 12 hours.

Let's define the total distance traveled by him as \(D\) km. Since Ajay walks halfway at his original speed and the remaining half at twice the speed, we can divide the total journey into two equal parts of \(\frac{D}{2}\) km each.

For the first half of the journey, where Ajay walks at 4 km/hr:

\( \text{Time for first half} = \frac{\frac{D}{2}}{4} = \frac{D}{8} \, \text{hours}\)

For the second half of the journey, where his speed is 8 km/hr:

\( \text{Time for second half} = \frac{\frac{D}{2}}{8} = \frac{D}{16} \, \text{hours}\)

The total time taken for the whole journey is 12 hours. Therefore, we sum the two times and equate to 12:

\(\frac{D}{8} + \frac{D}{16} = 12\)

To solve for \(D\), find a common denominator:

\(\frac{2D}{16} + \frac{D}{16} = 12\)

\(\frac{3D}{16} = 12\)

By solving the equation for \(D\), we multiply both sides by 16:

\(3D = 192\)

\(D = \frac{192}{3} = 64\)

Therefore, the total distance traveled by Ajay is 64 km.

Correct Answer: 64 km