# 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:

Two vessels of equal volume contain milk and water in the ratio 1:3 and 2:1. If they are mixed together, what is the new ratio?

 A) 11:13 B) 13:11 C) 9:11 D) 11:9

Explanation:

4 568
Q:

In a bucket, paint and oil are in the ratio 7 : 5. 24 litres of mixture is drawn off and 24 litres of oil is added. If the ratio of paint and oil becomes 1 : 1, then how many litres of paint was contained in the bucket initially?

 A) 49 B)  63 C)  84 D) 98

Explanation:

0 564
Q:

Rahul adds 2 litres of alcohol in 6 litres of water and Dinesh adds 1 litres of alcohol in 9 litres of water. What is the ratio of the percentage of alcohol in the two mixtures?

 A) 7 : 4 B) 2 : 1 C) 5 : 2 D) 8 : 3

Explanation:

4 554
Q:

The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?

 A)  3 : 5 B)  5 : 7 C) 3) 1 : 1 D)

Explanation:

0 537
Q:

Vipin adds 3 litres of liquid A in 6 litres of liquid B and Mohit adds 8 litres of liquid A in 15 litres of liquid B. What is the ratio of the percentage of liquid B in the two mixtures?

 A) 26 : 25 B) 51 : 32 C) 46 : 45 D) 34 : 25

Explanation:

5 503
Q:

25 litres of a mixture contains 30% of spirit and rest water. If 5 litres of water be mixed in it, the percentage of spirit in the new mixture is

 A) 45% B) 33 1/3% C) 25 % D) 12 1/2%

Explanation:

4 493
Q:

The ratio of sand to gravel in a mixture is 17 : 9 while that between gravel and cement is 6 : 17. What is the ratio of sand to cement in the mixture?

 A) 289 : 54 B) 9 : 6 C) 17 : 17 D) 2 : 3

Explanation:

2 459
Q:

In a mixture of 165 litres, the ratio of liquids X and Y is 6 : 5. If 5 litres of liquid Y is added in the mixture, then what is the ratio of X and Y in the new mixture?

 A) 10 : 9 B) 8 : 7 C) 9 : 8 D) 5 : 4