A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.
He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
(4 marks)

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Solution

Consider steps moved down being represented by positive integers and then, steps moved up are represented by negative integers.

(1 mark)

Initially monkey is sitting on the top most step i.e., first step

In 1^st jump monkey will be at step = 1 + 3 = 4th step

In 2^nd jump monkey will be at step = 4 + (-2) = 4 – 2 = 2nd step

In 3^rd jump monkey will be at step = 2 + 3 = 5th step

In 4^thjump monkey will be at step = 5 + (-2) = 5 – 2 = 3rd step

In 5^th jump monkey will be at step = 3 + 3 = 6th step

In 6^th jump monkey will be at step = 6 + (-2) = 6 – 2 = 4th step

In 7^th jump monkey will be at step = 4 + 3 = 7th step

In 8^th jump monkey will be at step = 7 + (-2) = 7 – 2 = 5th step

In 9^thjump monkey will be at step = 5 + 3 = 8th step

In 10^th jump monkey will be at step = 8 + (-2) = 8 – 2 = 6th step

In 11^th jump monkey will be at step = 6 + 3 = 9th step

(2 marks)

∴Monkey took 11 jumps to reach the water level at the 9^th step

(1 mark)

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(4 marks)