Question

A monkey tries to jump up a 50 m high pole. It jumps up 1.25 m every second, but slides down by 0.5m next second. In how many seconds it will reach the top ?

• A. 133
• B. 131
• C. 134
• D. 132

Answer 1

Answer:

B. 131

Understanding the Monkey Jump Problem

• Problem Type: This is a classic mathematical puzzle that tests logical reasoning and problem-solving skills, often seen in competitive exams under quantitative aptitude sections.

• Key Concept: The core idea is to calculate the net progress made by the monkey in a two-second cycle and then determine how many such cycles are needed to reach the top, considering the final jump.

Step-by-Step Calculation

• Net Progress per Cycle:

  • In the first second, the monkey jumps up by 1.25 m.

  • In the second second, it slides down by 0.5 m.

  • Therefore, the net upward movement in a 2-second cycle is 1.25 m - 0.5 m = 0.75 m.

• Approaching the Top: The pole height is 50 m. The monkey needs to reach a point from where its final jump of 1.25 m will take it to the top. This point is 50 m - 1.25 m = 48.75 m from the bottom.

• Cycles to Reach 48.75 m:

  • To cover 48.75 m with a net progress of 0.75 m per 2-second cycle, we divide: 48.75 m / 0.75 m/cycle = 65 cycles.

  • The time taken for these 65 cycles is 65 cycles * 2 seconds/cycle = 130 seconds.

• Final Jump: After 130 seconds (completing 65 cycles), the monkey is at a height of 48.75 m. In the next second (the 131st second), it makes its final jump of 1.25 m.

• Total Time: 130 seconds (for the cycles) + 1 second (for the final jump) = 131 seconds.