Question

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?

a) 5
b) 6
c) 7
d) 8

Answer 1

The monkey reaches the water level after 8 jumps down and returns to the top step with 4 jumps up. Negative and positive integers are used to represent downward and upward movements, respectively. The multiple-choice answer provided does not match the calculations, presuming it refers to the number of jumps to return to the top, which is 4.

Step-by-step explanation:

The question involves a series of mathematical steps to solve a problem related to the movement of a monkey and the representation of those movements using integers. It requires understanding sequences and arithmetic operations.

Part (i)

The monkey jumps 3 steps down and then 2 steps up. With each complete jump sequence, the monkey effectively moves 1 step down (3 down and 2 up: 3-2=1). The water level is at the ninth step, and the monkey is at the first step. To reach the water level (8 steps away, since 9-1=8), the monkey must repeat this complete sequence 8 times.

Part (ii)

After drinking the water, the monkey jumps 4 steps up and then 2 steps back down in each move. Thus, each complete sequence results in a net gain of 2 steps (4-2=2). To reach the topmost step again, 8 steps above the water level, the monkey must repeat this sequence 4 times.

Part (iii)

In this integer representation, the sum of (-3+2-...) indicates a downward movement, hence the sum of -8 shows the monkey has moved 8 steps down. Conversely, the sum of (4-2+...) being 8 represents moving up 8 steps.

The answer to the student's multiple-choice question is (c) 7, assuming it corresponds to the number of jumps required to return to the top step, which is 4. However, from the information provided, it is unclear how the choices presented relate to the actual calculations in the question.