Question

10. 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

Answer:

i) 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

thus, sum 8 in (b) represents going up by eight steps

Step-by-step explanation: