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 on the ninth step.
i) He jumps 3 steps down and then jumps back 2 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 (i) and (ii) by completing the following
a) −3 + 2 − ... = −8
b) 4 – 2 + …. = 8
In (a) the sum (−8) represents going down by 8 steps. So, what will the sum 8 in (b) represent?

Answer 1

Hint:For the first and second part, find the step the monkey is on after each jump, for ex: First jump = 1 + 3 = 4 steps, Second jump = 4 – 2 = 2 steps, and so on. When you reach the required step, then stop and count the number of jumps made. This method will help to eliminate any chances of mistakes.

Complete step-by-step answer:
In this question, the number of steps going up and down are known for both the cases.

i) Monkey jumps 3 steps down and then back 2 steps up. The jumps of monkey can be represented as:
First jump = 1 + 3 = 4 steps
Second jump = 4 – 2 = 2 steps
Third jump = 2 + 3 = 5 steps
Fourth jump = 5 – 2 = 3 steps
Fifth jump = 3 + 3 = 6 steps
Sixth jump = 6 – 2 = 4 steps
Seventh jump = 4 + 3 = 7 steps
Eighth jump = 7 – 2 = 5 steps
Ninth jump = 5 + 3 = 8 steps
Tenth jump = 8 – 2 = 6 steps
Eleventh jump = 6 + 3 = 9 steps
Monkey will reach ninth step in 11 jumps.

ii) Monkey jumps 4 steps up and then jumps back 2 steps down in every move. The jumps of monkey can be represented as follows:
First jump = 9 – 4 = 5 steps
Second jump = 5 + 2 = 7 steps
Third jump = 7 – 4 = 3 steps
Fourth jump = 3 + 2 = 5 steps
Fifth jump = 5 – 4 = 1 step
The monkey will reach back the top step after 5 jumps.

iii) Moves in part (i): - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 – 3 = -8 which represents the monkey going down by 8 steps.
Moves in part (ii): 4 – 2 + 4 – 2 + 4 = 8, the sum 8 in (b) represents the monkey goes up by 8 steps.

Note: In this question, it is important to note that in the first case you might think that in every 2 jumps, the monkey descends one step. So, it will take 16 jumps. But that is not true as at the 11th jump he descends 3 steps and reaches the 8th step and so it will not go back 2 steps. Similarly in the second case, it will take him 5 jumps instead of 8 jumps. Keep this in mind to avoid making any mistakes.