Question

5. 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?

Answer 1

Step-by-step explanation:

1st jump 1+3=4th\ step1+3=4th step

2nd jump 4-2=\ 2nd\ step\4−2= 2nd step

3rd jump 2+3=5th\ step\2+3=5th step

4th jump 5-2=\ 3rd\ step\5−2= 3rd step

5th jump 3+3=6th\ step3+3=6th step

6th jump 6-2=4th\ step6−2=4th step

7th jump 4+3=7th\ step\4+3=7th step

8th jump 7-2\ =\ 5th\ step\7−2 = 5th step

9th jump 5+3=\ 8th\ step\5+3= 8th step

10th jump 8-2=\ 6th\ step\8−2= 6th step

11th jump 6+3=\ 9th\ step\6+3= 9th step

he will reach 9th step in 11th jumps.

(ii) 1st jump = 9-4=\ 5th\ step\9−4= 5th step

2nd jump = 5+2=\ 7th\ step5+2= 7th step

3rd jump = 7-4=\ 3rd\ step\7−4= 3rd step

4th jump = 3+2=\ 5th\ step\3+2= 5th step

5th jump = 5-4=\ 1st\ step\5−4= 1st step

he reach back on the first step in fifth steps.

(iii)

(a) -3+2-3+2-3+2-3+2-3+2-3+2-3+2-3+2=\ -8−3+2−3+2−3+2−3+2−3+2−3+2−3+2−3+2= −8

(b) 4-2+4-2+4-2+4-2=\ 84−2+4−2+4−2+4−2= 8