A frog tries to come out of a dried well 4.5 m 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) 29

The depth of the dried well is 4.5 m, which is equal to 450 cm. In each jump, the frog jumps up 30 cm and slides down 15 cm. Therefore, the net effective height covered in one complete jump cycle is 30 cm - 15 cm = 15 cm. In such problems, we must account for the final jump where the frog reaches or crosses the top and does not slide back down. The remaining distance before the final jump where the frog can clear the well in one single jump of 30 cm is 450 cm - 30 cm = 420 cm. To cover a height of 420 cm at a net rate of 15 cm per jump, the number of jumps required is 420 / 15 = 28 jumps. After these 28 jumps, the frog reaches a height of 420 cm. On the 29th jump, the frog jumps up 30 cm, reaching 420 + 30 = 450 cm, which brings it completely out of the well. Thus, the total number of jumps required is 29. Therefore, option b is the correct answer.