# 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:

Wheat costing Rs 30/kg, Rs 35/kg and a third variety of wheat are mixed in the ratio of 3 : 4 : 2. If the mixture is costs Rs 34/kg, then what will be the cost (in Rs/kg) of the third variety of wheat?

 A) 46 B) 42 C) 32 D) 38

Explanation:

5 857
Q:

Two water squash mixtures, the first with a water-to-squash ratio of 5:1 and the letter with a ratio of 3:1 are blended in the ratio 3:2. What is the final water : squash ratio in the blend?

 A) 4:1 B) 10:9 C) 5:3 D) 6:1

Explanation:

2 819
Q:

A mixture of alcohol and water contains 7% alcohol. How much mixture (in litres) is required to get 357 litres of alcohol?

 A) 6300 B) 4200 C) 4900 D) 5100

Explanation:

2 814
Q:

A mixture of 50 kg of cement and gravel contains 10% of gravel. How many kg of gravel must be added to make the gravel content 28% in the new mixture?

 A) 14.5 B) 10.5 C) 12.5 D) 17.5

Explanation:

3 812
Q:

In a mixture, sugar and milk are in the ratio 4 : 5. If 7 litres of milk is added to it, then the ratio of sugar and milk in the new mixture becomes 2 : 3. What is the total quantity (In litres) of sugar in new mixture?

 A) 35 B) 28 C) 42 D) 24

Explanation:

3 792
Q:

Two vessels of equal capacity contains juice and water in the ratio of 5 : 1 and 5 : 7 respectively. The mixture of both the vessels are mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?

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

Explanation:

3 789
Q:

A shop keeper purchased 15 kg of sugar and 20 kg of wheat at Rs. 50 and Rs. 75 per kg respectively. On selling them, he gained 10% on sugar and 20% on wheat. What was the total sale vale?

 A) Rs. 2550 B) Rs. 2625 C) Rs. 1800 D) Rs. 1575

Explanation:

1 766
Q:

Ramesh uses a weight of 930 gm instead of 1 kg and sells sugar on its cost price. What will be his profit percentage on selling 15 kg sugar?

 A) 9.21 B) 7 C) 7.53 D) 8.54