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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 move in part (t) 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?



Answer -

(i) The position ofmonkey after the

1st jump J1 is at 4th step ↓
2nd jump J2 is at 2nd step ↑
3rd jump J3 is at 5th step ↓
4th jump J4 is at 3rd step ↑
5th jump J5 is at 6th step ↓
6th jump J6 is at 4th step ↑
7th jump J7 is at 7th step ↓
8th jump J8 is at 5th step ↑
9th jump J9 is at 8th step ↓
10th jump J10 is at 6th step ↑
11th jump J11 is at9th step ↓(Water level)
Hence the required number of jumps = 11.

(ii) Monkey’s positionafter the

1st jump J1 is at 5th step ↑
2nd jump J2 is at 7th step ↓
3rd jump J3 is at 3rd step ↑
4th jump J4 is at 5th step ↓
5th jump J5 is at 1st step ↑
Hence, the required number of jumps = 5.

(iii) According to thegiven conditions we have the following tables

Jumps

J1

J2

J3

J4

J5

J6

J7

J8

J9

J10

J11

Number of steps

-3

+2

-3

+2

-3

+2

-3

+2

-3

+2

-3

Therefore (a) Totalnumber of steps
=-3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3
= -8 which represents the monkey goes down by 8 steps.
In case (ii), we get

Jumps

J1

J2

J3

J4

J5

Number of steps

+ 4

-2

+4

-2

+4

Therefore (b) Totalnumber of steps.
= +4 – 2 + 4 – 2 + 4 = 8
Here, the monkey is going up by 8 steps.

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