Aspire Faculty ID #4336 · Topic: NIMCET 2017 · Just now
NIMCET 2017

caterpillar crawls up a pole of 75 inches high standing from the ground. Each day is crawls up 5 inches and each night it slides down 4 inches. When will it reach the top of the pole?

Solution

Caterpillar Climbing Problem

Pole height = 75 inches
Climbs up = 5 inches/day
Slides down = 4 inches/night

Net climb per day (after sliding): 5 - 4 = 1 inch

On the last day, caterpillar reaches the top without sliding back.

So, after n days, it reaches or passes 75 inches.

At the start of the nth day, it has climbed:

(n - 1) × 1 = n - 1 inches

On the nth day, it climbs 5 inches:

(n - 1) + 5 ≥ 75

Solving for n:

n - 1 + 5 ≥ 75
n + 4 ≥ 75
n ≥ 71

Answer: The caterpillar reaches the top on the 71st day.

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