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

Answer 1

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.