Question

After reaching the roof he wants to go back at the floor. For this, he moves 3 steps down and then back 1 step up in every move. In how many moves will he reach back the lowest steps? * 21 steps are there​

Answer 1

Answer:

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 move. 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 – 3 = -8 which represents the monkey going 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.

Answer 2

Answer:

In 10 moves he will reach to the lowest step.

Step-by-step explanation:

From floor to the roof there are total 21 steps. While he goes back, he moves 3 steps down and then 1 step up.

• In first move, from the roof he is at (3 - 1) = 2nd step.
• In second move, he is at {(2 + 3) -1} = 4th step.
• In third move, he is at {(4 + 3) -1} = 6th step.
• In fourth move, he is at {(6 + 3) -1} = 8th step.
• In fifth move, he is at {(8 + 3) -1} = 10th step.
• In sixth move, he is at {(10 + 3) -1} = 12th step.
• In seventh move, he is at {(12 + 3) -1} = 14th step.
• In eighth move, he is at {(14 + 3) -1} = 16th step.
• In ninth move, he is at {(16 + 3) -1} = 18th step.
• In tenth move, he is at {(18 + 3) -1} = 20th step.

By this type of movement he maximum can reach to 20th step and to reach there he needs to do 10 movements.

[Simpler way: He move 2 steps down in 1 movement

                      He move 20 steps down in 20/2 = 10 movements]

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