Each of the three pails A,B and C contains some water. The following steps are taken : (cont'd)?

Question

Step 1) 1/4 of the water in Pail A is poured into Pail B.
Step 2) 1/4 of the water in Pail B is poured into Pail C.
Step 3) 1/4 of the water in Pail C is poured into Pail A.
In the end, all the pails contain 18 litre of water each. Find the amount of water in each pail at first.

Answer 1

This is complicated.

Pail A pours first, then receives.
Pails B and C receive first, then pour.

Since each pail pours 1/4 of its contents, that means that for pails B and C, before pouring the amount of water they have is:

(4/3)*18 = 24

Pail C pours into pail A the amount of

24 - 18 = 6

This means that after pouring A had 18 - 6 = 12.

Before pouring then A had

(4/3)*12 = 16

So after receiving (1/4)16 = 4 from pail A. Pail B had 24. So pail B started with

24 - 4 = 20

So after receiving (1/4)24 = 6 from pail B. Pail C had 18. So pail C started with

24 - 6 = 18

So pails A, B, and C started with

A = 16 liters
B = 20 liters
C = 18 liters

Answer 2

Hi,

Neat problem!

A has 16, B has 20, and C has 18.

3/4a + 1/4(c + 1/4(b + 1/4a)) = 18 in A at the end
This is 3/4 of original A plus 1/4 of C added back to A

3/4(b + 1/4a) = 18
This is the remaining 3/4 of the original B plus the 1/4 of the original A that was poured into B

3/4( C + 1/4(B + 1/4A)) = 18
This is 3/4 of the original C plus 1/4 of what was poured from B into C to get 18.

These simplify into
49/64A + 1/16B + 1/4C = 18
3/16A + 3/4B = 18
3/64A + 3/16B + 3/4C = 18

Putting these ugly equations into a 3 x 4 matrix on my calculator, I used the rref matrix command to get my answers of 16, 20, and 18.

I hope that helps!

Answer 3

Pail A= 16 Liters
Pail B= 20 Liters
Pail C= 18 Liters

At last I got you man.
It is a best one I ever had.

Answer 4

Pail A is 3/4x+1/4times21/16x and pail B is 5/4minus 5/4times1/4 and pail c is 21/16x. if X is 18 litres, then :
pail A is: (21/64+3/4) 18 = 19.40625 litres
pail B is: 5/4 minus 5/16 times 18 = 16.875 litres
pail C is: 21/16 times 18 = 23.625

Man, that's probably the most complicated question I've ever seen. Is my answer correct?

Answer 5

B + 1/4A - 1/4(B + 1/4A) = 18
C + 1/4(B + 1/4A) - 1/4(C + 1/4(B + 1/4A)) = 18
3/4A + 1/4(C + 1/4(B + 1/4A)) = 18

Let's multiply all this by 16:

16B + 4A - 4B - A = 288
16C + 4B +A - 4C - B - 1/4A = 288
12A + 4C + B + 1/4A = 288

Now let's simplify each equation:

3A + 12B = 288
A + 4B = 96

3/4A +3B + 12C = 288
A + 4B + 16C = 384

49A + 4B + 16C = 1152

Using matrix method:

a) 1 4 0 96
b) 1 4 16 384
c) 49 4 16 1152

b-a:
0 0 16 288

0 0 1 18

c-b:
48 0 0 768

1 0 0 16

Since A=16 and C=18, and A+B+C=54
B=20

Answer 6

18 litres?