Question

Deep inside a jungle, a deer and a tiger are joyfully playing with one another. The deer notices that it is 40 steps away from the tiger and starts running towards it. At the same time, the tiger starts running away from the deer. Both run on the same straight line. For every five steps the deer takes, the tiger takes six. However, the deer takes only two steps to cover the distance that the tiger covers in three. In how many steps can the deer catch the tiger?

• A. 200
• B. 180
• C. 150
• D. 320
• E. 240

Hint:

Convert step lengths to a common measure (e.g., tiger steps) to compare speeds.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves calculating relative speeds based on step frequency and step length.
Step 2: Key Formula or Approach:
Standardize the unit of distance (step length). Let Deer's step length be \(D\) and Tiger's be \(T\).
Step 3: Detailed Explanation:
1. Step Length Ratio: 2 deer steps = 3 tiger steps \(\implies 1 D = 1.5 T\). 2. Relative Speed (in Tiger steps): In the time the deer takes 5 steps, it covers \(5 \times 1.5 = 7.5\) tiger steps. In that same time, the tiger takes 6 steps (\(6 \times 1 = 6\) tiger steps). 3. Relative speed of deer = \(7.5 - 6 = 1.5\) tiger steps per time unit (of 5 deer steps). 4. Initial gap = 40 deer steps = \(40 \times 1.5 = 60\) tiger steps. 5. Time units to catch = \(60 / 1.5 = 40\) time units. 6. Number of deer steps = 40 units \(\times\) 5 steps per unit = 200 steps.
Step 4: Final Answer:
The deer catches the tiger in 200 steps.