question_answer 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 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; \[\left( \text{a} \right)-\text{3}+\text{2}-\] ...... \[~=-\text{ 8 }\left( \text{b} \right)\text{ 4}-\text{2}+\] ...... = 8. In (a) the sum (- 8) represent going down by eight steps. So, what will the sum 8 in (b) represent?                

Answer:

                (i)   \[\left( -\text{3} \right)+\text{2}=-\left( \text{3}-\text{2} \right)=-\text{1}\] Since, the water level is at the eight step, therefore, he will reach the water level in 8 jumps. (ii) \[(+\text{ }4)+(-2)=4-2=2\] \[2+2+2+2=8\] Therefore, he will be out of the tank in 4 jumps. (iii) (a) \[-\text{ 3}+\text{2}+\left( -\text{ 3} \right)+\text{2}+\left( -\text{ 3} \right)\]\[+\text{2}+\left( -\text{ 3} \right)\]\[+\text{2}+\]\[\left( -\text{3} \right)+\text{2}+\left( -\text{ 3} \right)+\text{2}+\left( -\text{ 3} \right)+\text{2}+\left( -\text{ 3} \right)\] \[a+2=-8\] (b) \[\text{4}-\text{2}+\text{4}-\text{2}+\text{4}-\text{2}+\text{4}-\text{2}=\text{8}\] The sum 8 in (b) will represent going up.