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? 

(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; (a) – 3 + 2 – ... = – 8 (b) 4 – 2 + ... = 8. In (a) the sum (– 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

(i) Given that, a monkey is sitting at the topmost place of the water tank. But the water is in the ninth step. 

Here, the monkey moves three steps down and then, jumps back to two steps up.

To find the number of steps the monkey jumps to reach the water level.

Let us consider the steps jumps down be a positive integer. And the steps jumps up be a negative integer.

In 1^st jump, the monkey will be at step $= 1 + 3 = 4$ 

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

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

In 4^th jump, the monkey will be at step $= 5 + (-2) = 5 – 2 = 3$ 

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

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

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

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

In 9^th jump, the monkey will be at step $= 5 + 3 = 8$ 

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

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

Hence, the Monkey took 11 jumps to reach the water level