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?
- (a) 28
- (b) 29 ✓ UPSC's answer
- (c) 30
- (d) 31
Why the answer is (b)
• The well is 4.5 m deep, which equals 450 cm.
• In each jump, the frog climbs 30 cm but slides down 15 cm, resulting in a net gain of 15 cm per cycle.
• The frog must reach a height of at least 450 cm to escape; once it reaches or exceeds this height during a jump, it does not slide back.
• To find the number of jumps, consider that after (n-1) jumps, the frog must be at a height such that the next jump (30 cm) takes it to or above 450 cm.
• Let the height after (n-1) full cycles be H. We need H + 30 >= 450, so H >= 420 cm.
• Since each full cycle gives a net gain of 15 cm, the number of full cycles (n-1) required to reach 420 cm is 420 / 15 = 28 cycles.
• Therefore, the frog makes 28 full cycles (ending at 420 cm) and then makes one final jump to reach 450 cm, totaling 28 + 1 = 29 jumps.
Why the other options are wrong
- (a) 28
- 28 jumps would only reach a height of 420 cm, which is still 30 cm short of the well's depth.
- (c) 30
- 30 jumps is incorrect because the frog escapes on the 29th jump, making the 30th jump unnecessary.
- (d) 31
- 31 jumps is incorrect because the frog escapes on the 29th jump, making the 31st jump unnecessary.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.