Number of eggs laid on each day = Number of hens in the poultry farm = 60.
Out of the eggs laid on each day, the number of eggs t h a t got rotten is either 2 or 3 or 4.
Out of the eggs laid on each day, the number of eggs that got broken is either 4 or 5 or 6.
Maximum possible number of eggs taken to the market for sale on day 1 = 60 – (2 + 4)
= 54.
Minimum possible number of eggs taken to the market for sale on day 1 = 60 – (4 + 6)
= 50.
The minimum number of eggs that are left unsold each day must be 5, as the number of eggs that are rotten and broken among them needs to be an integer. It can be at max 10, since number of egg left unsold on any day is lessthan 20% ofthe number of eggs laid on each day, i.e. 20% of 60 = 12.
So, the number of eggs that are sold on day 1 ranges from (50 – 10 = 40) to (54 – 5 = 49), (both inclusive).
On the next day again 60 eggs are laid, so from the above logic the range of number of eggs sold should again come out to be from 42 to 49 (both inclusive), but there are eggs that remain unsold at the end of the previous day.
Minimum possible number of eggs that are left over from the previous day and are taken along with the eggs laid on a day to the market for sale = 5 – (40% of 5) – (2% of 5) = 2.
Maximum possible number of eggsthat are left over from the previous day and are taken along with the eggs laid on a day to the market for sale = 10 – (40% of 10) – (20% of 10) = 4.
So, the range of number of eggs that are sold on day 2 varies from (40 + 2 = 42) to (49 + 4 = 53) (both inclusive) and this holds true for day 3, day 4 and day 5 also,
The minimum possible number of eggs that were sold on day 4 can be 42, 42 eggs are sold in the scenorio when 10 eggs are left unsold.
So, the next day i.e. day 5, the minimum number of eggs that were sold can be calculated as Out of the 60 eggs that were laid – maximum rotten and broken eggs can be removed which are 4 and 6 respectively. Thus, left with 50 eggs. Also, from the 10 eggs of the previous day maximum rotten and broken can be removed which are 4 and 2 respectively, thus left with 4 eggs only. So, out of the total 54 eggs, a maximum of only 10 eggs can be left unsold. Therefore, the minimum eggs thatwere sold on day 5 were 54 – 10 = 44.
Hence, aggregate sum of eggs is 42 + 44 = 86.
Note: Most of the students will make a mistake of considering 42 eggs for both the days but this is not possible on any two consecutive days simultaneously.