A water tank has steps inside it . A monkey is sitting on the topmost 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 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) and the sum (-8) represent going down by eight steps. So, what will the sum in(b) represent?
Answers
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Step-by-step explanation:
What is the known?
Number of steps going up and down.
What is unknown?
In how many jumps will he reach the water level and In how many jumps will he reach back the top step?
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.