NIMCET 2008 — Reasoning PYQ

1. Visualizing the Movement:

• Initial Drop: The ball falls $16\text{ m}$.

• First Bounce: It goes up $8\text{ m}$ (half of $16$) and comes down $8\text{ m}$. Total for this bounce: $16\text{ m}$.

• Second Bounce: It goes up $4\text{ m}$ (half of $8$) and comes down $4\text{ m}$. Total for this bounce: $8\text{ m}$.

• This pattern continues infinitely.

2. Forming the Series:

The total distance $D$ can be written as:

3. Applying the Formula:

The terms inside the bracket $[16+8+4+\dots ]$ form an infinite geometric series where:

• First term $a=16$

• Common ratio $r=\frac{1}{2}$ (which is less than $1$)

The sum of an infinite GP is given by:

Substituting the values:

4. Total Distance Calculation:

Now, add the initial drop to the sum of the bounces:

Final Answer:

The total distance travelled by the ball is 48 m. Therefore, the correct option is (c).