Q9--------------A hen lays 3 eggs every day .....................?

Question

Q9--------------A hen lays 3 eggs every day ,one of which hatches and produces a hen the same day.The newly formed hen can start laying eggs from the next day at the same rate as the previous hen and so on.for all the hens that are produced.the other two eggs laid by the first hen hatch on the second day and produces hens which can start laying eggs from the next(third) day at the same rate as the older hens.This process goes on and on.After how many days(minimum) are there 100 unhatched eggs.
a. 12
b. 10
c. 20
d. 6

Answer 1

Iteration:
(egg-laying hen, new hen, eggs) = (a0, b0, c0) = (1, 0 , 0)
(a_n+1, b_ n+1, c_n+1) = (an + bn, an + bn + cn, 2an + 2bn)

days: (an, bn, cn)
1: (1 ,1 ,2)
2: (2 , 4 , 4)
3: (6 ,10,12)
4: (16,28,32)
5: (44,76,88)
6: (120,208,240) ... exceeds hundred.

thus after 6 days.


d:

Answer 2

Day 1 ------- H + H + E + E = 2 H + 2 E
2 --------------4 H + 8 E + 2 H + 2 H + 4 E = 8 H + 12 E
3 ------- - 8 H + 8 H + 32 E + 12 H + 12 H + 48 E = 40 H + 80 E
4 -------- 40 H + 40 H + 80 E + 80 H + 160 E = 240 E
on the 4th day more than 100 unhatched eggs are there.

Answer 3

The equation for the amount hens would be: previous hens X 2 + previous unhatched eggs.

And the equation for the amount of unhatched eggs would be: previous hens X 2

These rules don't work on day one.

So then we could make a chart:

Days, Hens, Unhatched eggs
...1.........2.........2
...2.........6.........4
...3........16.......12
...4........44.......32
...5.......120......88
...6.......328......240

As you can see, the 6 days is the minimum amount of days it takes to have at least 100 eggs, thus the answer is:

D

Answer 4

day 1
1 hen lays 3 eggs, 1 of which hatches immediately, making
2 hens
2 eggs
day 2
2 hens lay 6 eggs, 2 of which hatches immediately, making 4 hens. 2 eggs hatch making
6 hens
4 eggs
day 3
6 hens lay 18 eggs, 6 of which hatch immediately, making 12 hens. 4 eggs hatch making
16 hens
12 eggs
day 4
16 hens lay 48 eggs, 16 of which hatch immediately, making 32 hens and 32 eggs. 12 eggs hatch making 44 hens
day 5
44 hens lay 132 eggs, 44 of which hatch immediately, making 88 hens and 88 eggs. 32 eggs hatch making 120 hens
day 6
120 hens lay 360 eggs, 120 of which hatch immediately, making 240 hens and 240 eggs. 88 eggs hatch making 328 hens

On day 6 there are 240 unhatched eggs.

Answer 5

d) 6 days

Format:
A(hens) number of hens to lay eggs
B(0) Number of eggs that will hatch today
C(1) Number of eggs that are laid today that will hatch tomorrow
D(2) Number of eggs that are laid today that will hatch 2 days from today

Day one has 1(hen), 1(0), 1(1), 1(2) = 2 eggs (note the 1(0) egg hatches today)
Day two has 2(hen), 3(0), 3(1), 2(2) = 5 eggs (note the 3(0) eggs hatch today)
Day three has 5(hen), 8(0), 7(1), 5(2) = 12 eggs (note the 8(0) eggs hatch today)
Day four has 13(hen), 20(0), 18(1), 13(2) = 31 eggs (note the 20(0) eggs hatch today)
Day five has 33(hen), 51(0), 46(1), 33(2) = 79 eggs (note the 51(0) eggs hatch today)
Day six has 84(hen), 130(0), 117(1), 84(2) = 201 eggs (note the 130(0) eggs hatch today)

Answer 6

The answer is d, on the 6th day. The laid unhatched egg will 240 on that day.

Answer 7

12 days

Answer 8

D.
6 days.

Answer 9

a.12

Answer 10

a.12 is the min number of days