Question

In search of water, a frog fell down into a 30m deep well. Its progress out of the well was very erratic. Each day it managed to climb up 3m, but the following night, it slipped back 2m. How many days did it take to get out of the well?

Answer 1

Hint: It is given that the frog climbed up 3m in the daytime but fell down 2m at night. Therefore, the effective distance covered by the frog in a day should be equal to 3-2=1 m. Therefore, it will take 27 days to climb up 27m. However, on the 28th day, the frog would climb up 3m in the daytime and get out of the well, and once it gets out of the well, we should not consider that it would fall 2m again at night as it would have already gone out.

Complete step-by-step answer:
It is given that the distance climbed by the frog during daytime=3m
The distance by which the frog falls during night=2m
Therefore,
the effective distance covered by the frog in a day
=the distance climbed by the frog during daytime - The distance by which the frog falls during night
=3m-2m=1m
Thus, effectively the frog takes one day to climb one meter. Therefore, it should take $ 27\times 1 $ days to climb up 27m……………………(1.1)
However, on the 28th day, once the frog climbs up 3m in the daytime, it will get out of the well……….(1.2)
Therefore, from (1.1) and (1.2), we see that the number of days required for the frog to get out of the well = Time taken to climb 27m+ 1day to ascend 3m during daytime
=27days+1 day=28days
Thus, the required answer is 28 days.

Note: We should not consider that the effective length travelled by the frog on all days is 1m because it just needs to reach the top of the well, which it does on the daytime of 28th day. Therefore, after the 28th day’s daytime, we should not consider that it would fall 2m again at night as it would have already gone out.