A frog tries to come out of a dried well 4.5m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?

Correct Option (B)

The depth of the well is 4.5 m, which is equivalent to 450 cm.

In each jump, the frog ascends 30 cm but then slides down 15 cm. Therefore, the net upward progress for each jump, except the final one, is 30 cm - 15 cm = 15 cm.

On the final jump, the frog reaches the top of the well and does not slide back down. Let 'x' be the total number of jumps required.

The total distance covered can be represented by the sum of the upward movements from all 'x' jumps minus the downward slides from 'x-1' jumps (as there is no slide after the last jump). This must equal the total depth of the well.

The equation is set up as follows:

$$30x-15(x-1)=450$$

Solving the equation:

$$30x-15x+15=450$$

$$15x+15=450$$

$$15x=450-15$$

$$15x=435$$

$$x=\frac{435}{15}$$

$$x=29$$

Therefore, the frog requires 29 jumps to come out of the well.

Incorrect Options:

Option (A) 28: If the frog made 28 jumps, the total height covered would be $30\times 28-15\times (28-1)=840-15\times 27=840-405=435$ cm. This is less than the well's depth of 450 cm, indicating 28 jumps are insufficient.

Option (C) 30: This answer would be obtained if one incorrectly assumes a net gain of 15 cm on every single jump, including the last one, leading to $450÷15=30$ jumps. This overlooks the fact that the frog does not slide down after the final jump when it exits the well.

Option (D) 31: If the frog made 31 jumps, the total height covered would be $30\times 31-15\times (31-1)=930-15\times 30=930-450=480$ cm. This exceeds the well's depth, meaning the frog would have exited before completing 31 jumps.