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:

(i) He jumps 2 steps down and then jumps back 1 step up. In how many jumps will he reach the water level?

(ii) After drinking water, he want to go back. For this, he jumps 3 steps up and 1 step down in every move. In how many jumps will he reach the top level?

Given: A monkey is sitting on the topmost step (i.e. the first step). The water level is at the ninth step.

To find: 

(i) He jumps 2 steps down and then jumps back 1 step up. In how many jumps will he reach the water level?

(ii) After drinking water, he want to go back. For this, he jumps 3 steps up and 1 step down in every move. In how many jumps will he reach the top level?

Solution:

i) Monkey jumps 3 steps down and then back 2 steps up. The jumps of monkey can be represented as:–

First jump = 1 $+$ 3 = 4 steps

Second jump = 4 $-$ 2 = 2 steps

Third jump = 2 $+$ 3 = 5 steps

Fourth jump = 5 $-$ 2 = 3 steps

Fifth jump = 3 $+$ 3 = 6 steps

Sixth jump = 6 $-$ 2 = 4 steps

Seventh jump = 4 $+$ 3 = 7 steps

Eighth jump = 7 $-$ 2 = 5 steps

Ninth jump = 5 $+$ 3 = 8 steps

Tenth jump = 8 $-$ 2 = 6 steps

Eleventh jump = 6 $+$ 3 = 9 steps

So, Monkey will reach ninth step in 11 jumps.

ii) Monkey jumps steps up and then jumps back 2 steps down in every move. The jumps of monkey can be represented as follows:–

First jump = 9 $–$ 4 = 5 steps

Second jump = 5 $+$ 2 = 7 steps

Third jump = 7 $–$ 4 = 3 steps

Fourth jump = 3 $+$ 2 = 5 steps

Fifth jump = 5 $–$ 4 = 1 step

So, the monkey will reach back to the top step after 5 jumps.

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Updated on: 10-Oct-2022

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