10. A water tank has steps inside it. A monkey is sitting on the topmost step ie the first
step. The water level is at the ninth step.
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 lie 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 in
by completing the following: (a) - 3 - 2 -
(b) 4-2 + ... = 8. In (a) the sum - 8 represents going
down by eight steps. So, what will the sum 8 in (b
represent?
Answers
Answer:
Steps:
i) Monkey jumps
3
steps down and then back
2
steps up. The jumps of monkey can be represented as:–
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
steps
Eleventh jump
=
6
+
3
=
9
steps
Monkey will reach ninth step in
11
jumps.
ii) Monkey jumps
4
steps up and then jumps back
2
steps down in every ove. The jumps of monkey can be represented as follows;–
First jump
=
9
–
4
=
5
steps
Second jump
=
5
+
2
=
7
steps
Third jump
=
7
–
4
=
3
steps
Fourth jump
=
3
+
2
=
5
steps
Fifth jump
=
5
–
4
=
1
step
The monkey will reach back the top step after
5
jumps.
iii) Moves in part (i)
[
−
3
+
2
−
3
+
2
−
3
+
2
−
3
+
2
−
3
+
2
=
−
8
]
which represents the monkey goes down by
8
steps
Moves in part (ii)
4
–
2
+
4
–
2
+
4
=
8
,
the sum
8
in (b) represents the monkey goes up by
8
steps.