mathematics question

1) Q=P(1+50%) = 1.5P

&R=Q(1+50%) = 1.5P(1.5) = 2.25P

Hence, P:R = 1:2.25 = 4:9

2) Let the cost px of an egg is $x.
then selling px of a dozen of egg is $15x
hence, the % profit is,
($15x-$12x)/$12x * 100% = 25%

3) base area of the cylinder will be π(8/2)^2 cm^2 = 16π cm^2
volumn of 6 metallic balls = 6 * π(2)^3 cm^3 = 48π cm^3

Hence, the rise in water level
= 48π cm^3 / 16π cm^2
= 3 cm
hence, the water level rise 3cm after the balls are put.

1}If Q exceeds P by 50%

Q=(1+50%)P=1.5 P

and R exceeds Q by 50%,

R=(1+50%)Q=1.5 Q=1.5 * 1.5 P= 2.25 P

find P:R.

R=2.25P
P/1 = R/ 2.25

So, P:R = 1: 2.25=4:9

2}The selling price (S) of a dozen of eggs is equal to the cost price(C) of 15 eggs.Find the precentage profit.

12S=15C
S=5/4 C= (1+25%)C

So, the precentage profit=25%

3}A right cylinder container 8cm in base diameter (2R) contains water.6 metallic balls of radii(r) 2 cm are put into the container.If all the balls are immersed and no water overflows,find the rise in water level(L)

volume rised= volume of the balls
volume rised= pi* R^2 * L
volume of the balls= 4/3 pi* r^3 *6
R=8/2=4
r=2

16L=4/3 *8 * 6
L=4

As we are using cm in all quantities, the unit of L is also cm.
the rise in water level= 4 cm