Question

On the bank of the pristine Tunga river, a deer and a tiger are joyfully playing with each other. 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. To solve this, the length of a deer’s step must also be given.
• C. 120
• D. 360
• E. 320

Answer 1

The Correct Option is A

Step 1: Relation between step lengths 
From the problem: “the deer takes 2 steps to cover the distance that the tiger covers in 3.” 
So, if the tiger’s one step = 3 units, then the deer’s one step = 1.5 × tiger’s step. 
Let tiger’s step = 3 units → deer’s step = 4.5 units.

Step 2: Relation between number of steps taken
For every 5 steps of deer, the tiger takes 6 steps. 
So, in the same duration: 
Deer covers = 5 × 4.5 = 22.5 units
Tiger covers = 6 × 3 = 18 units

Step 3: Effective approach of deer
Since both move in opposite directions (deer towards tiger, tiger away), the net gain of the deer in closing the gap = 22.5 − 18 = 4.5 units every cycle (i.e., 5 steps of deer).

Step 4: Initial gap
The initial distance = 40 steps of deer = 40 × 4.5 = 180 units.

Step 5: Time to catch
Deer closes 4.5 units in 5 steps. 
Therefore, to close 180 units: 
Number of deer steps = (180 ÷ 4.5) × 5 = 40 × 5 = 200 steps.

Final Answer:

The deer catches the tiger in 200 steps.