NIMCET 2024 — Reasoning PYQ

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Question

NIMCET 2024 — Reasoning PYQ

NIMCET | Reasoning | 2024

A cat climbs a 21- meter pole. In the first minute it climbs 3 meter and in the second minute it descends one meter. In how minutes the cat would reach the top of the pole ?

Choose the correct answer:

Explanation

This is a classic arithmetic puzzle involving alternating progress. The most crucial trick to remember is that once the cat reaches the top of the pole, it does not slip back down.

Step 1: Set aside the final jump

Total height of the pole = $21 meters$
Height climbed in the final positive attempt = $3 meters$

To avoid calculating slips after the goal has been achieved, subtract the final minute's climb from the total height:

$Remaining height to analyze = 21 - 3 = 18 meters$

Step 2: Find the net progress in a single cycle

Let us calculate how much net height the cat covers during its standard repeating cycle:

$1^{st}$ minute: Cat climbs $+ 3 meters$
$2^{nd}$ minute: Cat slips down $- 1 meter$

$Net distance covered = 3 - 1 = 2 meters$

$Total time taken for this progress = 1 + 1 = 2 minutes$

So, the net progress is $2 meters$ every $2 minutes$ .

Step 3: Calculate time required to reach the safe height ( $18 meters$ )

Since the cat climbs a net height of $2 meters$ in a $2 minute$ block, we calculate the number of cycles required to reach at least $18 meters$ :

$Number of cycles = \frac{18 meters}{2 meters/cycle} = 9 cycles$

Now, multiply the cycles by the time length of each cycle:

$Time taken for 9 cycles = 9 \times 2 minutes = 18 minutes$

At exactly $18 minutes$ , the cat has securely reached a height of $18 meters$ .

Step 4: Add the final step

In the next minute (the $1 9^{th}$ minute), it is the cat's turn to make a positive climb again.

Current height = $18 meters$
Distance covered in the next $1 minute$ = $+ 3 meters$

$Final Height = 18 + 3 = 21 meters$

The cat reaches the exact top ( $21 meters$ ) at the end of this minute, so it will not slip back.

$Total time required = 18 minutes + 1 minute = 19 minutes$

Correct Answer:

The correct option is (C) 19 min.