Discussion
A person has to touch the top of a tower of 60 feet height. In every second, he climbs 5 feet, but slips down 4 feet. In how many seconds would he touch the top ?
Answer: A
He touches the top in 56 seconds.
Each second he gains 5 feet but slips back 4, a net gain of 1 foot. The trap is the last climb: once he is within 5 feet of the top, the next climb takes him there and he does not slip back.
\[ \begin{aligned} \text{height before last climb} &= 60 - 5 = 55\ \text{ft} \\ \text{time to reach 55 ft} &= 55 \times 1 = 55\ \text{s} \\ \text{total} &= 55 + 1 = 56\ \text{s} \end{aligned} \]
60 seconds treats every second as a net gain of 1 foot right to the top, ignoring that the final climb ends the task.
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