A deep well 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. If the monkey jumps 3 steps down and then jumps back 2 steps up, how many jumps does it have to make to reach the water level?

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Solution

The correct option is A
11

Assume jumping downwards as positive and jumping upwards as negative.
Its given that the monkey is sitting on the first step.
To reach the second step, the monkey will jump twice i.e. (+3) + (-2) = 1 (as x+(-y) = x-y)
$\Rightarrow$ To reach the third step, the monkey will again jump twice i.e. (+3)+(-2) = 1 (as x+(-y) = x-y)
$\Rightarrow$ To reach the fourth step, the monkey will again jump twice i.e. (+3)+(-2) = 1 (as x+(-y) = x-y)
$\Rightarrow$ To reach the fifth step, the monkey will again jump twice i.e. (+3)+(-2) = 1 (as x+(-y) = x-y)
$\Rightarrow$ To reach the sixth step, the monkey will again jump twice i.e. (+3)+(-2) = 1 (as x+(-y) = x-y)
Now, the monkey has reached sixth step.
It will jump three steps down then, it will reach ninth step.
So, the total jumps can be given as [(+3) + (-2)] + [(+3) + (-2)] + [(+3) + (-2)] + [(+3) + (-2)] + [(+3) +(-2)] + (+3)
= 3-2+3-2+3-2+3-2+3-2+3 = 11
Therefore the required number of jumps to reach ninth step is 11.

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