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# Alligation or Mixture Questions

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A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

A6 litres

B1 litres

C8 litres

D7 litres

Explanation:

Milk in 1 litre mixture in 1st can = 3/4 litre.
Milk in 1 litre mixture in 2n d can = 1/2 litre.
Milk in 1 litre final mixture = 5/8 litre.
By rule of alligation we have required ratio 5 : 8

3/4 1/2

\ /
(5/8)

/ \

1/8 : 1/8

Therefore ratio of two mixtures =1/8:1/8=1:1
So, quantity of mixture taken from each can =(1/2)*12= 6 litres

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A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30 / kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

A1 kg

B3 kgs

C5 kgs

D10 kgs

Explanation:

A=20/kg,B=24/kg ,C =30/kg

lets assume x kg be rice A,
y kg be rice B
and 2 kgs is rice C

Given final CP = 25

So, 20x+24y+60=25(x+y+2) ------(1)

By Solving above eq. y=10-5x

Since , y cannot be zero or negative
Hence, x can only be 1 giving y = 5kg

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There are two bottles A and B, each filled with milk and water in the ratio 5:3 and 1:2 respectively. A new mixture is formed by mixing the contents of A and B in the ratio 4:3.What is the ratio of composition of milk and water in the new mixture?

A1:3

B1:2

C1:1

D3:2

Explanation:

Bottle A mixture: milk = 5/8 & water=3/8
Bottle B mixture: milk = 1/3 & water=2/3

Given New mixture (Bottle A & B) ratio = 4:3

Now milk ratio = (5/8*4/7) + (1/3*3/7) = 1/2
and water = (3/8*4/7) + (2/3*3/7) = 1/2

So, New mixture ration milk : water = 1 : 1

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A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

A550 kg.

B400 kg.

C600 kg.

D650 kg.

Explanation:

Profit on 1st part Profit on 2nd part:
8% 18%
\ /
Mean Profi 14%
/ \
4 6
Ratio of 1st and 2nd parts = 4 : 6 = 2 : 3
Quantity of 2nd kind = (3/5 ) * 1000 kg = 600 kg

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A coffee seller has two types of coffee Brand A costing 5 bits per pound and Brand B costing 3 bits per pound. He mixes two brands to get a 40 pound mixture. he sold this at 6 bits per pound. the seller gets a profit of 33 1/2 percent. how much he has used Brand A in the mixture?

A33 pounds

B25 pounds

C30 pounds

D35 pounds

Explanation:

Let x and y quantities of A and B respectively are mixed.
=> x+y=40 --------- (1)
His total selling price = 40*6=240
His cost price 180 approx(as he makes 33.5 % profit)
5x+3y=180 ------------- (2)
On solving (1) and (2)
x=30 pounds.

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If a and b are mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is 35 liters, find the amount of b?

A13.34

B15.73

C16.73

D9.45

Explanation:

a:b:c,then b ratio is b/(a+b+c)*35

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5 coffee and 4 tea costs Rs.96, 5 badam milk and 6 coffee costs Rs. 32 and 7 tea and 6 badam milk costs Rs.37. What is the combined price of 1 tea, 1 coffee and 1 badam milk?

A12

B15

C20

D16

Explanation:

Acc. to the question:
5c+4t=96 ----- (i)
5b+6c=32 ----- (ii)
7t+6b=37 ----- (iii)
11c+11b+11t=165
b+c+t= 15Rs

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If a Strawberry and a Butterscotch together cost Rs. 18.00, a Vanilla and a Strawberry cost Rs. 9.00 and a Butterscotch cost Rs.9.00 more than a Vanilla or a Strawberry then which of the following can be the price of a Butterscotch?

ARs. 13.5

BRs.10

CRs. 12

DRs. 13

Explanation:

Acc. to the question
S+B= 18 ---- (1)
V+S= 9 ---- (2)
B-S=9 ---- (3)
Adding (1) and (3) we get
2B= 27 so B= 13.5Rs

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Two beakers are on the table. The capacity of the first beaker is x liters and that of the second beaker is 2x liters. Two thirds of the first beaker and one fourth of the second beaker is filled with wine. The remaining space is filled with water. If the content in both the beakers are mixed in a large beaker of volume 3x liters, what is the proportion of wine in the beaker?

A12/11

B11/36

C7/6

D7/18

Explanation:

capacity of beakers x,2x,3x
2/3(x)+1/4(2x)=7x/6
wine proportion is =7x/(6*3x)=7/18

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A manufacturing company has 15% cobalt ,25% led and 60% of copper. If 5kg of led is used in a mixture, how much copper we need to use:

A12 kg

B14 kg

C10 kg

D9 kg

Explanation:

25%=5kg
100%=20kg
60% of 20 kg= 12 kg

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