# Model 10 Percentage With Allegations & Mixture Practice Questions Answers Test With Solutions & More Shortcuts

#### PERCENTAGE PRACTICE TEST [11 - EXERCISES]

Question : 16 [SSC CGL Prelim 2007]

1 litre of water is added to 5 litres of alcohol-water solution containing 40% alcohol strength. The strength of alcohol in the new solution will be

a) 33\$1/3\$%

b) 30%

c) 33%

d) 33\$2/3\$%

Alcohol in original solution = \$40/100 × 5\$ = 2 litres

Water in original solution = 3 litres

On adding 1 litre water, water becomes 4 litres.

Now, 6 litres of solution contains 2 litres of alcohol.

100 litres of solution contains = \$2/6 × 100\$

= \$100/3 = 33{1}/3%\$ alcohol.

Question : 17

In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength ?

a) 3 : 1

b) 1 : 2

c) 1 : 3

d) 2 : 1

Let x litres of first mixture is mixed with y litres of the second mixture.

According to the question,

\${x × 30 /100 + y × 50/100}/{x × 70/100 + y × 50/100} = 45/55\$

\${0.3x + 0.5y}/{0.7x + 0.5y} = 9/11\$

6.3x + 4.5y = 3.3x + 5.5y

6.3x – 3.3x = 5.5y – 4.5y

3x = y ⇒ \$x/y = 1 : 3\$

Question : 18

An ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. To obtain 60 kg of pure iron, the quantity of the ore needed (in kgs) is approximately :

a) 300

b) 250.57

c) 266.67

d) 275.23

In 4 kg of ore, iron = 0.9 kg.

Quantity of ore for 60 kg of iron

= \${60 × 4}/0.9\$ = 266.67 kg

Question : 19

A litre of pure alcohol is added to 6 litres of 30% alcohol solution. The percentage of water in the solution is

a) 40%

b) 50%

c) 65%

d) 60%

In 30% alcohol solution,

Alcohol = \$30/100 × 6\$ =1.8litres

Water = 4.2 litres

On mixing 1 litre of pure alcohol,

Percentage of water =\$4.2/7 × 100\$ = 60%

Question : 20

A sample of 50 litres of glycerine is found to be adulterated to the extent of 20%. How much pure glycerine should be added to it so as to bring down the percentage of impurity to 5% ?

a) 149 litres

b) 155 litres

c) 150 litres

d) 150.4 litres

Glycerine in mixture = 40 litres

Water = 10 litres

Let x litres of pure glycerine is mixed with the mixture.

\${40 + x}/{50 + x} = 95/100 = 19/20\$

800 + 20x = 950 + 19x

x = 950 – 800 = 150 litres.

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