Question

A monkey can jump three steps forward in a single hop and two steps backward in another hop every time. How many times does the monkey hop to reach the thirtieth step if it starts from the first step?

• A. 53
• B. 10
• C. 45
• D. 58

Answer 1

The correct option is A 53

Initially, the monkey is at step 1.

When it jumps forward, it reaches step 4, and then it jumps 2 steps backward, thereby coming back to step 2.

So, in 2 hops, it reaches step 2.

When it jumps forward from step 2, it reaches step 5, then it jumps 2 steps backward, thereby coming back to step 3.

So, in a total of 4 hops, it reaches step 3.

∴ The monkey follows the expression: $Numberofhops=2\times (Stepnumber-1)$

This process continues till it reaches step 27. From the 27${}^{th}$ step, when it jumps 3 steps forward in 1 hop, it reaches the 30${}^{th}$ step.

To reach step 27, it will take
= 27 × (2 – 1) = 52 hops.

∴ It requires 53 hops to reach the 30${}^{th}$ step.