  Ncert solutions

# Question 9

Q10) 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? Solution 10:

(i) 1st jump 1+3=4th\ step

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

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

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

5th jump 3+3=6th\ step

6th jump 6-2=4th\ step

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

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

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

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

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

he will reach 9th step in 11th jumps.

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

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

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

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

5th jump = 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

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

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

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