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: Let the deer's step length = $D$, tiger's step length = $T$. Given: $2D = 3T \implies D = 1.5T$.
Step 2: Speeds: Deer takes 5 steps in same time tiger takes 6 steps. Deer's speed = $5D$ per unit time, Tiger's speed = $6T$ per unit time. But $D = 1.5T$, so deer's speed = $5 \times 1.5T = 7.5T$, tiger's speed = $6T$. Relative speed = $7.5T - 6T = 1.5T$ per unit time.
Step 3: Initial distance = 40 deer steps = $40D = 40 \times 1.5T = 60T$.
Step 4: Time to catch = $\frac{60T}{1.5T} = 40$ units of time.
Step 5: In 40 units, deer takes $5 \times 40 = 200$ steps.
Step 6: Final Answer: 200.