Question

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 move 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) represent going down by eight steps. So, what will the sum 8 in (b) represent?

Answer 1

(i)He jumps 3 steps down and jumps back 2 steps up. Following number ray shows the jumps of monkey:

First jump = 1 + 3 = 4 steps  Second jump = 4 – 2 = 2 steps

Third jump = 2 + 3 = 5 steps Fourth jump = 5 – 2 = 3 steps

Fifth jump = 3 + 3 = 6 steps   Sixth jump = 6 – 2 = 4 steps

Seventh jump = 4 + 3 = 7 steps  Eighth jump = 7 – 2 = 5 steps

Ninth jump = 5 + 3 = 8 steps  Tenth jump = 8 – 2 = 6 step

Eleventh jump = 6 + 3 = 9 steps 

He will reach ninth steps in 11 jumps.

(ii)     He jumps four steps and them jumps down 2 steps. Following number ray shows the jumps of monkey:

Thus monkey reach back on the first step in fifth jump.

(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.