# 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:

In a mixture of 45 litres, the ratio of liquid A and liquid B is 7 : 2. If 11 litres of liquid B is added to the mixture, then what will be the ratio of liquid A and liquid B in the new mixture?

 A) 7 : 4 B) 8 : 5 C) 6 : 5 D) 5 : 3

Explanation:

4 719
Q:

In what ratio must a mixture of 11% sugar strength be mixed with that of 25% sugar strength so as to get a new mixture of 13% sugar strength?

 A) 5:1 B) 6:1 C) 7:2 D) 10:3

Explanation:

1 681
Q:

In a mixture 25 liters, the ratio of milk and water is 4:1. How many liters of milk must be added to make the ratio 16:1?

 A) 21 B) 25 C) 60 D) 36

Explanation:

6 678
Q:

Two water-squash mixtures, the first having a water-to-squash ratio of 4 : 1 and the other having a ratio of 3 : 1, are blended in the ratio 1 : 2. What is the water : squash ratio in the blend?

 A) 19:11 B) 23:7 C) 17:13 D) 4:3

Explanation:

3 675
Q:

35% of an alloy was silver. If in the quantity of alloy there was 119 g of silver, what was the quantity of the elements in the alloy?

 A) 273 g B) 204 g C) 221 g D) 340 g

Explanation:

0 650
Q:

In what ratio rice costing Rs 14/kg mixed with another rice costing Rs 11/kg to get the mixture costing Rs 11.6/kg?

 A) 2 : 5 B) 1 : 4 C) 1 : 3 D) 1 : 5

Explanation:

5 631
Q:

A mixture contains liquid A and liquid B in the ratio of 5 : 4. If 2 litres of liquid B is added to it, then the ratio of liquid A and liquid B becomes 7 : 6. What is the quantity (in litres) of liquid A in the mixture?

 A) 32 B) 35 C) 40 D) 42

Explanation:

1 581
Q:

In what ratio wheat costing Rs 17/kg mixed with another wheat costing Rs 12/kg to get a mixture costing Rs 13.5/ kg?

 A) 1 : 2 B) 2 : 5 C) 3 : 7 D) 4 : 9