Question

A water tank has steps inside it. A monkey is sitting on the topmost step (first step). The water level is at 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?

Lesson :- Integers
Class 7, mathematics


• Answer all the questions.
• Explain briefly.
• Step by step explanation required. ​

Answer 1

Given :-

A water tank has steps inside it. A monkey is sitting on the topmost step (first step). The water level is at 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 :-

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

Total steps to water level = 9

No. of steps he jumped = 3

No. of steps he came back = 2

Hence, He moved forward we should substract the steps.

= 9 - 3

= 6

And Then he jumps 2 steps back. So, we should add the steps.

= 6 + 2

= 8

In 8 jumps the monkey will reach the water level ( 9th step ).

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(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?

Total steps to water level = 9

No. of steps he jumped up = 4

No. of steps he step down = 2

Hence, he moves 4 steps up.

= 9 - 4

= 5

But he moves 2 times every move. So, He would be in the 9th step.

Therefore, he should move 8 steps up.

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(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:

In (a) the sum (-8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

(a) - 3 + 2 - ___ = - 8

= -3 + 2 = -1

-8 - (-1)= 8 + 1 = 9

Answer = 9

(b) 4 - 2 + ___ = 8

This 8 represents going up.

= 4 - 2 = 2

8 - 2 = 6

Answer = 6

Answer 2

$\large\underline{\bf{Solution-}}$

Let the steps be represented by Ist step, 2nd step, 3rd step and so on to 9th step from top to bottom

Answer :- (i)

According to statement,

He jumps 3 steps down and then jumps back 2 steps up.

So,

After

$\rm :\longmapsto\: {1}^{st} \: jump \: he \: is \: at \: {4}^{th} \: step$

After,

$\rm :\longmapsto\: {2}^{nd} \: jump \: he \: is \: at \: {2}^{nd} \: step$

After,

$\rm :\longmapsto\: {3}^{rd} \: jump \: he \: is \: at \: {5}^{th} \: step$

After,

$\rm :\longmapsto\: {4}^{th} \: jump \: he \: is \: at \: {3}^{trd} \: step$

After,

$\rm :\longmapsto\: {5}^{th} \: jump \: he \: is \: at \: {6}^{th} \: step$

After,

$\rm :\longmapsto\: {6}^{th} \: jump \: he \: is \: at \: {4}^{th} \: step$

After,

$\rm :\longmapsto\: {7}^{th} \: jump \: he \: is \: at \: {7}^{th} \: step$

After,

$\rm :\longmapsto\: {8}^{th} \: jump \: he \: is \: at \: {5}^{th} \: step$

After,

$\rm :\longmapsto\: {9}^{th} \: jump \: he \: is \: at \: {8}^{th} \: step$

After,

$\rm :\longmapsto\: {10}^{th} \: jump \: he \: is \: at \: {6}^{th} \: step$

After,

$\rm :\longmapsto\: {11}^{th} \: jump \: he \: is \: at \: {9}^{th} \: step$

$\boxed{ \red{ \bf \:Hence \: the \: total \: number \: of \: jumps = 11}}$

Answer :- (ii)

According to statement,

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.

After,

$\rm :\longmapsto\: {1}^{st} \: jump \: he \: is \: at \: {5}^{th} \: step$

After,

$\rm :\longmapsto\: {2}^{nd} \: jump \: he \: is \: at \: {7}^{th} \: step$

After,

$\rm :\longmapsto\: {3}^{rd} \: jump \: he \: is \: at \: {3}^{rd} \: step$

After,

$\rm :\longmapsto\: {4}^{th} \: jump \: he \: is \: at \: {5}^{th} \: step$

After,

$\rm :\longmapsto\: {5}^{th} \: jump \: he \: is \: at \: {1}^{st} \: step$

$\boxed{ \red{ \bf \:Hence \: the \: total \: number \: of \: jumps = 5}}$

Answer :- (iii)

(a) According to statement,

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)

So,

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf J_1 & \sf - 3 \\ \\ \sf J_2 & \sf 2 \\ \\ \sf J_3 & \sf - 3\\ \\ \sf J_4 & \sf 2\\ \\ \sf J_5 & \sf - 3\\ \\ \sf J_6 & 2\sf \\ \\ \sf J_7 & \sf - 3\\ \\ \sf J_8 & \sf 2\\ \\ \sf J_9 & \sf - 3\\ \\ \sf J_{10} & \sf 2\\ \\ \sf J_{11} & \sf - 3 \end{array}} \\ \end{gathered}$

This implies,

Total number of steps taken by monkey is

= - 3 + 2– 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3

= - 8

which represents that the monkey goes down by 8 steps.

(b) According to statement,

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 (ii)

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf J_1 & \sf 4 \\ \\ \sf J_2 & \sf - 2 \\ \\ \sf J_3 & \sf 4\\ \\ \sf J_4 & \sf - 2\\ \\ \sf J_5 & \sf 4 \end{array}} \\ \end{gathered}$

This implies,

• Total number of steps taken by monkey is

• = + 4– 2 + 4 – 2 + 4

• = + 8

which represents that the monkey goes up by 8 steps.