Question

10 gallons are drawn from a container full of alcohol and filled
with water again. 10 gallons of mixture are again drawn and
the container is filled with water again. If the ratio of alcohol
and water left in the container is 49:32, the find how much
quantity does the container hold?​

Answer 1

Answer:

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Alligation or Mixtures - Aptitude test, questions, shortcuts, solved example videos

Online aptitude test >> Alligation or Mixtures - Aptitude test, questions, shortcuts, solved example videos

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Alligation and Mixtures

Important terms:

1) Alligation: Rule of alligation enables us to find the ratio in which two or more ingredients at a given price must be mixed to produce a resultant mixture of desired price.

2) Mean Price: It is the cost of unit quantity of a mixture.

3) Mixture: Mixture is formed by mixing two or more quantities. It can be expressed in the form of percentage or ratio.

- 10 % of sugar in water

- A solution of water and sugar is 12 : 20, which means water : sugar = 12 : 20

According to the rule of alligation: When two ingredients are mixed,

Cheaper Quantity (X) = (C.P. of Y) – (Mean Price)

(Quantity of Y) (Mean Price) – (C.P. of X)

If a vessel contains A liters of milk and if B litres of milk is withdrawn and replaced by water, and again if B litres of mixture is withdrawn and replaced by water and this operation is replaced n times in all, then

(Quantity of milk left after nth operation) = (A – B) n

(Initial quantity of milk) A

Quantity of milk left after nth operation = A x [A(1 – (B/A))n]

A

Simplified formula to calculate quantity of milk left after nth operation = [A(1 – (B/A))n]

Tricks and Tips:

1) Rule of alligation:

Ratio = (M – B) = (B – M)

(A – M) (M – A)

Points to Remember While Using the Rule of Alligation

- The three values alligated should always represent the same variable and should have same units.

- alligation of 3 values of cost gives the ratio in terms of number and vice-versa.

- If two values of cost price and selling price of the mixture are given, then in such cases first calculate the cost price of the mixture and then allegate the 3 values of cost price.

- A and B represent concentration if the numerical is based on mixing of solutions

Answer 2

Answer:

The capacity of the container will be 45 gallons.

Step-by-step explanation:

• The replacement formula

⇒ $( \frac{(x - a)}{x} )^{n} = \frac{Ratio of (New quantity)}{Initial Quanitity}$  where,

"x" represents the quantity of the container,

"a" represents the quantity drawn from the container and replaced with water or another thing.

"n" represents the number of times replacement is done.

• Given -      "a" = 10 gallons,  "n" = 2 times, Ratio = 49:81
• To find -     "x" = capacity of the container
• Solution -  Putting all the respective values in the formula we get,

        ⇒  $(\frac{x - 10}{x} )^{2} = \frac{49}{81}$

         ⇒ $(\frac{x - 10}{x} ) = \sqrt{ \frac{49}{81}}$

         ⇒ $(\frac{x - 10}{x} ) = \frac{7}{9}$

         ⇒ 9x - 90 = 7x

        ⇒ 9x - 7x = 90

        ⇒ 2x = 90

        ⇒ x = 45

Hence the capacity or quantity of the container can hold will be 45 gallons

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