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 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level? (ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?

Let’s assume that positive integers are used to represent the steps that are moved down. Negative integers are used to indicate the steps that were advanced.

(i) The monkey’s initial position was stepped = 1

The monkey will be at the step after the first jump. = 1 + 3 = 4

The monkey will be at the step after the second jump. = 4 + (−2) = 2

The monkey will be at the step after the third jump = 2 + 3 = 5

At step after the fourth jump, the monkey = 5 + (−2) = 3

The monkey will be at the step after the fifth jump = 3 + 3 = 6

At step after the sixth jump, the monkey = 6 + (−2) = 4

At step after the seventh jump, the monkey = 4 + 3 = 7

At step after the eighth jump, the monkey = 7 + (−2) = 5

At step after the ninth jump, the monkey = 5 + 3 = 8

The monkey will be at step after the tenth jump = 8 + (−2) = 6

The monkey will be at the step after the eleventh jump = 6 + 3 = 9

As a result, after 11 hops, the monkey will be at the water level (i.e., the ninth step).

(ii) At first, the monkey was at step = 9

Afte r 1st jump, the monkey will be at step = 9 + (−4) = 5

After 2nd jump, the monkey will be at step = 5 + 2 = 7

After 3rd jump, the monkey will be at step = 7 + (− 4) = 3

After 4th jump, the monkey will be at step = 3 + 2 = 5

After 5th jump, the monkey will be at step = 5 + (− 4) = 1

After five jumps, it is obvious that the monkey will

(iii) if negative integers are used to indicate steps taken back

Positive numbers are used to indicate the steps that were moved up, so his movements will be as follows.

Partially moves (i)

− 3 + 2 − 3 + 2 − 3 + 2 − 3 + 2 − 3 + 2 − 3 = −8

Moves in part (ii)

4 − 2 + 4 − 2 + 4 = 8

Moves in part (ii) denotes going up 8 steps.

Summary:

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 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level? (ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?

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 3 steps down and then jumps back 2 steps up. The monkey will reach the ninth step in 11 jumps

(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. The monkey will reach back to the top step after 5 jumps.