# Alligation or Mixture Questions

FACTS  AND  FORMULAE  FOR  ALLIGATION  OR  MIXTURE  QUESTIONS

I. Alligation : It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

II. Mean Price : The cost price of a unit quantity of the mixture is called the mean price.

III. Rule of Alligation : Suppose Rs.x per unit be the price of first ingradient mixed with another ingradient (cheaper) of price Rs.y per unit to form a mixture whose mean price is Rs. z per unit, then

Quantity of cheaper : Quantity of dearer

= ( C.P of dearer - Mean Price ) : ( Mean Price - C. P of cheaper )

= ( x- z ) : ( z - y )

IV. Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After  operations , the quantity of pure liquid = $x{\left(1-\frac{y}{x}\right)}^{n}$ units.

Q:

If a dairy mixes cow's milk which contains 10% fat with buffalo's milk which contains 20% fat, then the resulting mixture has fat (120/7)% of fat. What ratio was the cow's milk mixed with buffalo's milk?

 A) 2 : 5 B) 1 : 5 C) 2 : 3 D) 2 : 1

Answer & Explanation Answer: A) 2 : 5

Explanation:

6 1774
Q:

The ratio of milk and water in three samples is 1 : 3, 3 : 5 and 11 : 5. A mixture containing equal quantities of all three samples is made. What will be the ratio of milk and water in the new mixture?

 A) 7 : 9 B) 5 : 7 C) 15 : 13 D) 9 : 11

Answer & Explanation Answer: A) 7 : 9

Explanation:

8 1757
Q:

The ratio of sand to gravel in a mixture is 7 : 8 while that between gravel and cement is 6 : 7. What is the ratio of sand to cement in the mixture?

 A) 49 : 48 B) 7 : 7 C) 8 : 6 D) 3 : 4

Answer & Explanation Answer: D) 3 : 4

Explanation:

2 1752
Q:

Two bottles contain acid and water in the ratio 2 : 3 and 1 : 2 respectively. These are mixed in the ratio 1 : 3. What is the ratio of acid and water in the new mixture ?

 A) 7:13 B) 11:57 C) 23:37 D) 1:3

Explanation:

4 1741
Q:

The average age of 6 members of a family is 20 years. If the age of the servant is included, then the average age increase by 25%. What is the age (in years) of the servant?

 A) 30 B) 35 C) 50 D) 55

Explanation:

5 1716
Q:

In a colored picture of blue and yellow color, blue and yellow color is used in the ratio of 4:3 respectively. If in upper half, blue : yellow is 2:3, then in the lower half blue : yellow is

 A) 1 : 1 B) 2 : 1 C) 26 : 9 D) 9 : 26

Answer & Explanation Answer: C) 26 : 9

Explanation:

5 1663
Q:

A milk merchant buys 50 litres of milk at the rate of Rs 40 per litre and mixes 5 litres of water in it. If he sells this mixture at the rate of Rs 42 per litre, then what is the profit percentage for the dealer?

 A) 17.2 B) 14.4 C) 16.6 D) 15.5

Explanation:

7 1662
Q:

In two types of brass, the ratios of Copper to Zinc are 8:3 and 15:7 respectively. If the two types of brass be melted and mixed in the ratio 5:2 a new type of brass is obtained. The ratio of Copper to Zinc in this new type of brass is

 A) 3:2 B) 2:3 C) 3:4 D) 5:2