# 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 pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ?

 A) 11 lit B) 22 lit C) 33 lit D) 44 lit

Explanation:

Let the capacity of the pot be 'P' litres.
Quantity of milk in the mixture before adding milk = 4/9 (P - 8)
After adding milk, quantity of milk in the mixture = 6/11 P.
6P/11 - 8 = 4/9(P - 8)
10P = 792 - 352 => P = 44.

The capacity of the pot is 44 liters.

43 23853
Q:

In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 liters of pure milk , the percentage of milk in the mixture  become 76%. The quantity of mixture is:

 A) 65 liters B) 91 liters C) 38 liters D) None of these

Explanation:

Milk             Water

74%             26%        (initially)

76%             24%        ( after replacement)

Left amount = Initial amount

24  = 26$1-7k$

=> k = 91

51 23477
Q:

Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?

 A) 193 : 122 B) 97 : 102 C) 115 : 201 D) 147 : 185

Explanation:

Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total content = 3,5,7

Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3 = 35 , 105/5 = 21 , 105/7 = 15

Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)

i.e (35,70), (42,63), (45,60)

So overall mixture ratio of milk and water is

35+42+45 : 70+63+60

122:193

But in the question asked the ratio of water to milk = 193 : 122

30 21918
Q:

A container contains 40 litres of milk.From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container.

 A) 26.34 litres B) 27.36 litres C) 28 litres D) 29.16 litres

Explanation:

Amount of milk left after 3 operations

$401-4403=40*910*910*910=29.16$ litres

65 18229
Q:

A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km /hr. Find the distance travelled on foot ?

Let the Journey on foot be x km

Journey on cycle = (80 – x) km

=> x = 32km

Therefore,  Distance covered on foot in 4 hrs = ( 4 x 8) = 32 km

18084
Q:

In what ratio should two varieties of sugar at Rs.18 per kg and Rs.24 Kg be mixed together to get a mixture whose cost is Rs.20 per kg ?

= 4 : 2 = 2 : 1

Thus, the two varieties should be mixed in the ratio 2 : 1

17933
Q:

From a tank of petrol , which contains 200 liters of petrol, the seller replaces each time with kerosene when he sells 40 liters of petrol(or mixture). Everytime he sells out only 40 liters of petrol (pure or impure). After replacing the petrol with kerosene 4th time, the total amount of kerosene in the mixture is

 A) 81.92L B) 96L C) 118.08L D) None of these

Explanation:

The amount of petrol left after 4 operations = $200×1-402004=$81.92

Hence the amount of kerosene = 200 - 81.92 = 118.08 liters

23 17592
Q:

Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C.

 A) 1:9 B) 9:1 C) 3:7 D) 7:3

Explanation:

Ratio of Milk and water in a vessel A is 4 : 1

Ratio of Milk and water in a vessel B is 3 : 2

Ratio of only milk in vessel A = 4 : 5

Ratio of only milk in vessel B = 3 : 5

Let 'x' be the quantity of milk in vessel C

Now as equal quantities are taken out from both vessels A & B

=> 4/5     :     3/5
x
3/5-x          x - 4/5

=> $35-xx-45$ = $11$ (equal quantities)

=> x = 7/10

Therefore, quantity of milk in vessel C  = 7

=> Water quantity = 10 - 7 = 3

Hence the ratio of milk & water in vessel 3 is 7 : 3