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

Monkey Jumps 3 steps down and 2 steps up so, in total he jumped 1 step down.Therefore , Now he is at second step and water level is at the ninth step.

Now, he will reach water level in 9−2=7 jumps.

(b) He jumps 4 steps up and 2 steps down ,so totally he climbs 2 steps up in 6 Jumps,Similarly we can divide 9 steps as follows

⇒9=2+2+2+3

After reaching the third Step, As he jumps up 3 more Steps He will reach the top step and till then there will be no more steps to climb.(Means after 3 more Jumps he will reach the top step)

Now, the number of jumps he made to reach the top =2×6+2×6+2×6+3=12+12+12+3=39