A monkey ascends a greased pole 21 meters high. In the first minute he ascends 5 meters and in the next minute descends 3 meters. If he continues this process, in how many minutes will he reach the top?
The Usual Method
The total distance ascended by the monkey every 2 minutes = 5 – 3 = 2 meters. Hence to ascend 16 meters, he will take (2 minutes), i.e. 16 minutes.
(Note: We took 16 meters as the monkey ascends 5 meters every minute and has to ascend 21 – 5 = 16 meters.)
In the 17th minute the monkey climbs 5 meters. Hence 16 + 5 = 21 meters is when the monkey reaches the top.
(Note: Here the student is supposed to know the concept used to arrive at this answer using 16 meters.)
Estimated Time to arrive at the answer = 45 seconds.
The monkey climbs 5 – 3 = 2 meters every 2 minutes. Hence to climb 21 meters, he should take 21 minutes (purely looking at this relationship itself). Hence the answer should be 21 minutes. From the options, it can be either 17 or 18 minutes.
Checking for 18 minutes, we find that after 18 minutes, the monkey will be at 18 meters (Note: At even numbered minutes, the monkey will have climbed its numerical equivalent in height).
Checking for 17 minutes, we should first check for 16 minutes (refer to the above note). At 16 minutes, the monkey will climb 16 meters and in the next minute, it would climb 5 meters reaching 16 + 5 = 21 meters. Hence 17 meters is the answer.
Estimated Time to arrive at the answer = 15 seconds.