A logic problem by Rishabh Sood

Logic Level 2

Mr.Richard is quite an eccentric dairy farmer.

He originally had a total 54 gallons of milk in three churns and he wanted to make sure each churn contained 18 gallons of milk.

In order to do this, he did the following:

  • First he poured 1/4 of the first churn in the second churn.

  • He then poured 1/2 of the second churn into the third churn.

  • Finally he poured 1/3 of the third churn into the first churn.

How many gallons did each churn contain before Farmer Richard started pouring?

(input your answer in the order of the numbers,for example if your answer is 26,26,2 then type it as 26262)


The answer is 12339.

Rishabh Sood by Rishabh Sood , 20, India

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2 solutions

Rishabh Sood
Apr 8, 2016

  • Pour 1 C1 = 12(before) C1 = 9 (after) C2 = +3(therefore)

  • Pour 1 C2 = 33 (before) C2 = 36 (after)

  • Pour 2 C2 = 36 (before) C2 = 18 (after) C3 = +18(therefore)

  • Pour 3 C3 = 27 (before) C3 = 18 (after) C1 = +9(therefore)

  • Pour 3 C1 = 9 (before) C1 = 18 (after)

To explain a little further. After pour 3, C3 must have contained 18 gallons, so it must have contained 27 before the pour. Similarly after pour 2, C2 must have contained 18 gallons, so must have contained 36 before the pour. After pour 3, C1 must have contained 18 gallons, and it received 9 gallons from pour 3, so must have had 9 before the pour. So pour 1 left 9 gallons in C1, which means C1 contained 12 before the pour and C2 received 3 gallons. We know that C2 had 36 gallons before pour 2, so must have started with 33 gallons. QED!

3 Helpful 0 Interesting 1 Brilliant 0 Confused
Saya Suka
Mar 23, 2021

Let the original volumes be A, B & C.

(1 - 1/2)(B + A/4) = (1 - 1/3)(C + B/2 + A/8) = (1 - 1/4)A + (C + B/2 + A/8)/3

(B + A/4)/2 = 2(C + B/2 + A/8)/3 = 3A/4 + C/3 + B/6 + A/24
Multiply everything with 24

12B + 3A = 16C + 8B + 2A = 18A + 8C + 4B + A

A + 4B = 16C
16C + 8B + 2A = 18A + 8C + 4B + A
8C + 4B = 17A
16C + 8C + 4B = 17A + A + 4B
24C = 18A
4C = 3A
A + 4B = 4(4C) = 4(3A) = 12A
4B = 11A


A : C = 4 : 3 & B : A = 11 : 4
A : B : C = 4 : 11 : 3

4x + 11x + 3x = 54
18x = 54
x = 3

Answer
= A : B : C
= 4x : 11x : 3x
= 12 : 33 : 9
= 12339

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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