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# Alligation or Mixture Questions

NA
SHSTTON
40
Solv. Corr.
47
Solv. In. Corr.
87
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31 / 46

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A vessel is filled to its capacity with pure milk. Ten litres are withdrawn from it and replaced by water. This procedure is repeated again. The vessel now has 32 litres of milk. Find the capacity of the vessel (in litres).

A40 litres.

B50 litres.

C2 litres.

DNone of these

Explanation:

Lets assume the capacity of the vessel = x litres.
x (1- 10/x)^2 = 32
x^2 +100-20x = 32x
x^2 +100 - 52x= 0
x^2 - 50x - 2x + 100 = 0
=> (x-2) (x-50) = 0
=> x=2 & x=50
As 10 litres is withdrawn so vessel capacity will be 50 litres.

Workspace

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In a mixture of petrol and kerosene, petrol is only 99 litres. If this same quantity of petrol would be presented in another mixture of petrol and kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol In the present mixture would have been 13.33% point less than that. What is the concentration of petrol in actual mixture?

A20%

B16.66%

C26.66%

D8.33%

Explanation:

Lets assume amount of petrol = x
So, (x*100)/198=13.33
x=26.3934
Now same amount of petrol is in 99 liters also.
so the percentage in actual mixture is
(26.3934*100)/99 =26.66%

Workspace

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55
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85
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A juice container was 4/5 full. Ravinder poured 4 glasses from it and then poured two glasses back. The container is 3/4 full now. How many glasses can be filled if the entire container of juice is emptied?

A32

B36

C44

D40

Explanation:

first it was (4/5) 80% full then after filling 2 glass it is (3/4) 75% full
Thus every 5% means 2 glass
Therefore 100% can fill (100/5)*2 = 40 glasses

Workspace

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1/7 th of the tank contains fuel. If 22 litres of fuel is poured into the tank the indicator rests at 1/5th mark. What is the quantity of the tank?

A385

B358

C375

DNone of these

Explanation:

Lets assume the quantity of tank = x
x/7 + 22 = x/5
=> x/5-x/7 = 22
=> 2x/35 = 22 => x = 385

Workspace

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You need a 18% acid solution for a certain test, but your supplier only ships a 13% solution and a 43% solution. You need 120 lts of the 18% acid solution. the 13% solution costs Rs 82 per ltr for the first 67 ltrs, and Rs 66 per ltr for any amount in access of 67 ltrs. What is the cost of the 13% solution you should buy?

A8002

B7012

C7672

D7342

Explanation:

Let us assume we need "a" liters of 13% acid solution and "b" liters of 43% acid solution. Now
=>18 = (a * 13 + b * 43)/(a + b)
=>a/b = 5/1
So we need 100 liters of 13% acid solution, and 20 liters of 18% acid solution.
Final cost = 82 * 67 + 66 * 33 = 7672

Workspace

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Three containers A, B and C are having mixtures of milk and water in the ratio of 1:5, 3:5, 5:7 respectively. If the capacities of the containers are in the ratio 5:4:5, find the ratio of milk to water, if all the three containers are mixed together.

A53:115

B53:113

C54:115

D54:113

Explanation:

Assume that there are 500,400 and 500 litres respectively in the 3 containers.
Then, we have, 83.33, 150 and 208.33 litres of milk in each of the three containers.
Thus, the total milk is 441.66 litres. Hence, the amount of water in the mixture is
1400 - 441.66 = 958.33liters.
Hence, the ratio of milk to water is
441.66 : 958.33 => 53:115 (using division by .3333)
The calculation thought process should be
(441*2+2) : (958*3+1) = 1325 : 2875.
Dividing by 25 => 53:115.

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On a certain assembly line, the rejection rate for Hyundai i10s production was 4 percent, for Hyundai i20s production 8 percent and for the 2 cars combined 7 percent. What was the ratio of Hyundais i10 production?

A3/1

B2/1

C1-Jan

D1/2

Explanation:

4(i10s) 8(i20s)
7
3 1

production ratio = (3/4)/(1/4) = 3:1

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How many liters of a 90% of concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30 liter solution of 78% concentrated acid?

A3

B4

C6

D10

Explanation:

concentration is given which is wrt 100, hence we can take x lt of 90% and (30-x)of 75%
x*90 + (30-x)*75 = 30*78 hence the ans is 6 ltr.

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Eesha bought two varities of rice costing Rs. 50 per kg and Rs. 60 per kg and mixed them in some ratio. Eesha sold that mixture at Rs. 70 per kg making a profit of 20 %. What was the ratio of the micxture?

A1:5

B2:5

C5:1

DNone of these.

Explanation:

let x be the price of the rice after mixing
So, 120*x/100=70
x=175/3

By eligation method
the required ratio = (60-175/3) : (175/3-50) = 1:5

Workspace

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How many Kg of sugar must be added to 30 Kg of 2% solution of sugar and water to increase it to a 10% solution ?

A2.6Kg

B4Kg

C3.4Kg

D1.8Kg

Explanation:

In 30kg solution sugar is 2%
So finding out the quantity of sugar = 0.02*30= 0.6kgs
Now let x kgs of sugar be added to make 10% concentration
So (0.6+x)/(30+x) = 10/100
Solving we get x= 2.6kgs.

Workspace

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