an ant climbing up a vertical pole ascends 12 metres and slips down 5 metre in every alternate hour. If the pole is 63metres high how long will it take it to reach the top

Hi,

Consider the first hour: the ant goes up by 12 m. It slips down by 5 m in the second hour. So, effective distance climbed in the first 2 hours = 7 m
So, in 14 hours, the ant would have climbed 7*7 = 49 m
In the 15th hour, it climbs to 61 m and in the 16th hour, it slips down to 56 m.
Now, there is only 7 m to get to the top of the pole. Since the ant covers 12 m in one hour, it covers 7 m in 35 minutes.
So, at the end of 16 hours 35 minutes, the ant would reach the top of the pole.