A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4thfull

examrobotsa's picture

Submitted by examrobotsa on

Q: 142 (IAS/2010)
A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days the basket was 1/4thfull ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,5,5,2,1,2,5

keywords: 

{'successive day': [0, 0, 1, 0], 'eggs': [1, 0, 1, 0], 'basket': [0, 0, 1, 2], 'days': [0, 0, 2, 0], 'number': [0, 0, 0, 2], 'many days': [0, 0, 4, 1]}

The problem is about exponential growth where the number of eggs doubles each day. Given that the basket gets completely filled in 24 days, this means that it was half full the previous day (day 23), then quarter full two days before it was half full (day 22).

Option 1 suggests that the basket was 1/4 full on day 6, but that`s too early considering the growth rate. Option 2 implies the basket was 1/4 full on day 12, which is also far too early. Similarly, option 3 suggesting day 17 is not correct. The correct answer is option 4 because on day 22, the basket was 1/4 full, doubling to half-full on day 23, and then becoming completely filled on day 24.