# 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:

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

 A) 8:3 B) 6:7 C) 7:5 D) 11:7

Answer & Explanation Answer: C) 7:5

Explanation:

Milk in 1-litre mixture of A = 4/7 litre.

Milk in 1-litre mixture of B = 2/5 litre.

Milk in 1-litre mixture of C = 1/2 litre.

By rule of alligation we have required ratio X:Y

X                  :                 Y

4/7                                2/5

\                      /

(Mean ratio)
(1/2)

/                      \

(1/2 – 2/5)     :       (4/7 – 1/2)

1/10                      1/1 4

So Required ratio = X : Y = 1/10 : 1/14 = 7:5

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25 15031
Q:

In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?

 A) 24 lit B) 16 lit C) 32 lit D) 8 lit

Answer & Explanation Answer: C) 32 lit

Explanation:

Given mixture = 48 lit

Milk in it = 48 x 5/8 = 30 lit

=> Water in it = 48 - 30 = 18 lit

Let 'L' lit of water is added to make the ratio as 3:5

=> 30/(18+L) = 3/5

=> 150 = 54 + 3L

=> L = 32 lit.

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36 13861
Q:

In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?

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

Answer & Explanation Answer: A) 1:1

Explanation:

Quantity of alohol in the mixture = 40 x 5/8 = 25 lit

Quantity of water = 40 - 25 = 15 lit

According to question,

Required ratio =

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28 13622
Q:

How much pepsi at Rs.6 a litre is added to 15 litre of 'dew' at Rs. 10 a litre so that the price of the mixture be Rs.9 a litre?

 A) 5 B) 8 C) 10 D) None of these

Answer & Explanation Answer: A) 5

Explanation:

Let x litre pepsi is required.

(10-9)=1           :                3=(9-6)

Therefore  in 1:3 one part = 5

=>  x= 5 litres

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8 12939
Q:

In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?

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

Answer & Explanation Answer: C) 2:1

Explanation:

Given rate of wheat at cheap = Rs. 2.90/kg

Rate of wheat at cost = Rs. 3.20/kg

Mixture rate = Rs. 3/kg

Ratio of mixture =

2.90                              3.20

3

(3.20 - 3 = 0.20)            (3 - 2.90 = 0.10)

0.20 : 0.10 = 2:1

Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

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20 11570
Q:

There are two mixtures of honey and water in which the ratio of honey and water are as 1:3 and 3:1 respectively. Two litres are drawn from first mixture and 3 litres from second mixture, are mixed to form another mixture. What is the ratio of honey and water in it ?

 A) 111:108 B) 11:9 C) 103:72 D) None

Answer & Explanation Answer: B) 11:9

Explanation:

From the given data,

The part of honey in the first mixture = 1/4

The part of honey in the second mixture = 3/4

Let the part of honey in the third mixture = x

Then,

1/4             3/4

x

(3/4)-x     x-(1/4)

Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3

=> $34-xx-14=23$

=> Solving we get the part of honey in the third mixture as 11/20

=> the remaining part of the mixture is water = 9/20

Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .

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20 10786
Q:

A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is

 A) 1 : 10 B) 10 : 1 C) 9 : 11 D) 11 : 9

Answer & Explanation Answer: A) 1 : 10

Explanation:

Customer ratio of Milk and Water is given by

Milk          ::        Water

6.4                         0

$6411$

=> Milk : Water = 110 : 11 = 10 : 1

Therefore, the proportionate of Water to Milk for Customer is 1 : 10

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29 9636
Q:

If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain ?

 A) 25% B) 30% C) 17% D) 19%

Answer & Explanation Answer: A) 25%

Explanation:

He has gain = 15 - 12 = 3,
Gain% = (3/12) x 100 = (100/4) = 25.
He has 25% gain.

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19 9390