A water tank has steps inside it. A monkey is sitting on the first step. The water level is at the 9th step. he jumps 3 steps down and then jump back 2 steps up. In how many jump will be reach the water level?
Answers
i) Let us assume, down moved steps be represented by positive whereas up moved steps be represented by negative integers
It is given that,
Initially the monkey will be at step = 1
After the 1st jump monkey’s step = 1 + 3 = 4
After the 2nd jump monkey’s step = 4 + (-2) = 2
After the 3rd jump monkey’s step = 2 + 3 = 5
After the 4th jump monkey’s step = 5 + (-2) = 3
After the 5th jump monkey’s step = 3 + 3 = 6
After the 6th jump monkey’s step = 6 + (-2) = 4
After the 7th jump monkey’s step = 4 + 3 = 7
After the 8th jump monkey’s step = 7 + (-2) = 5
After the 9th jump monkey’s step = 5 + 3 = 8
After the 10th jump monkey’s step = 8 + (-2) = 6
After the 11th jump monkey’s step = 6 + 3 = 9
Hence,
From above results it is clear that the monkey will be at water level i.e.,9 after 11 jumps
(ii) From above, we have
Initial step of monkey = 9
Therefore,
After the 1st jump monkey’s step = 9 + (-4) = 5
After the 2nd jump monkey’s step = 5 + 2 = 7
After the 3rd jump monkey’s step = 7 + (-4) = 3
After the 4th jump monkey’s step = 3 + 2 = 5
After the 5th jump monkey’s step = 5 + (-4) = 1
Hence,
It is clear from the above results is that after 5 jumps the monkey will reach back at the top
(iii) If we will represent the down steps by negative and up steps by positive than the moves are are as follows:
We have,
Moves in (i):
- 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 = 8
Also,
Moves in part (ii):
4 – 2 + 4 – 2 + 4 = 8
Therefore,
Moves in part (ii) shows those steps who moves up.