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 to the top step?

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Solution

Step 1: Find the number of steps to reach the water level.
Let us assume that the steps moved down be denoted by positive integers.
The steps moved up be denoted by negative integers.
(i) Originally, the monkey was at step $= 1$
After $1^{s t}$ jump, the monkey will be at step $= 1 + 3 = 4$
After $2^{n d}$ jump, the monkey will be at step $= 4 + (- 2) = 2$
After $3^{r d}$ jump, the monkey will be at step $= 2 + 3 = 5$
After $4^{t h}$ jump, the monkey will be at step $= 5 + (- 2) = 3$
After $5^{t h}$ jump, the monkey will be at step $= 3 + 3 = 6$
After $6^{t h}$ jump, the monkey will be at step $= 6 + (- 2) = 4$
After $7^{t h}$ jump, the monkey will be at step $= 4 + 3 = 7$
After $8^{t h}$ jump, the monkey will be at step $= 7 + (- 2) = 5$
After $9^{t h}$ jump, the monkey will be at step $= 5 + 3 = 8$
After $10^{t h}$ jump, the monkey will be at step $= 8 + (- 2) = 6$
After $11^{t h}$ jump, the monkey will be at step $= 6 + 3 = 9$
Therefore, the monkey will be at water level (i.e., $9^{t h}$ step) after $11$ jumps.
Step 2: Find the number of steps to reach back to the top level.
(ii) At first, the monkey was at step $= 9$
After $1^{s t}$ jump, the monkey will be at step $= 9 + (- 4) = 5$
After $2^{n d}$ jump, the monkey will be at step $= 5 + 2 = 7$
After $3^{r d}$ jump, the monkey will be at step $= 7 + (- 4) = 3$
After $4^{t h}$ jump, the monkey will be at step $= 3 + 2 = 5$
After $5^{t h}$ jump, the monkey will be at step $= 5 + (- 4) = 1$
Clearly, the monkey will reach back at the top step after $5$ jumps.
Step 3: Find the number of steps moving in both conditions. by doing the direct calculation according to the sign.
(iii) If steps moved down are denoted by negative integers
The steps moved up are denoted by positive integers, then his moves will be as follows.
Moves in part (i)
$- 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3$
Moves in part (ii)
$4 - 2 + 4 - 2 + 4$
Hence, the monkey will be at water level (i.e., $9^{t h}$ step) after $11$ jumps.
and the monkey will reach back at the top step after $5$ jumps.

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Similar questions

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?

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Question 10(ii)
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.

(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 it reach back the top step?

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He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

A water tank has steps inside it. A monkey is sitting on the top most step (i.e., the first step). The water level is at the ninth step .

(1) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level ?

(2) 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 ?

(3) If the no. Of steps moved down is represented by negative integers and the no. Of steps moved up by positive integers , represent his moves in part 1 and 2 by completing the following; (1) -3+2-..... = -8 (2) 4-2+....... =8. In 1 the sum (-8) represent going down by eight steps. So, what will the sum 8 in 2 represent ?

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