On a vertical pole, a monkey climbs 30 feet in one hour and then rests for a while during which he slips down 20 feet. He again s…

Question

On a vertical pole, a monkey climbs 30 feet in one hour and then rests for a while during which he slips down 20 feet. He again starts climbing and slips back in the same manner. If he begins his ascent at 8 am, at what time will he first touch a flag on the pole at 120 feet from the ground?

1. A. 4 pm
2. B. 5 pm
3. C. 6 pm (Correct answer)
4. D. 7 pm

Correct Answer

Option C — 6 pm

Detailed Solution & Explanation

The correct answer is 6 pm.

Key Points

• Each cycle the monkey gains a net 10 feet — up 30, then slipping back 20 — and one cycle takes one hour.
• After 9 hours he has gained 9 × 10 = 90 feet, so at 5 pm he stands at 90 feet.
• In the 10th hour he climbs 30 feet from 90 and therefore touches 120 feet, at 6 pm, before any further slipping.

Additional Information

• The decisive point is that the question asks when he first touches 120 — the final climb counts even though he would slip back afterwards.
• Dividing 120 by the net gain of 10 gives 12 hours and the wrong answer; the last climb must always be handled separately in this question type.
• The general rule: subtract one full climb from the target, divide the remainder by the net gain, then add one more period.