# Mixture and Alligation Exercise 2

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- Question 1 of 19
##### 1. Question

In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?

##### Hint

In 1 kg mixture quantity of iron = 200 gm

Let x gm sand should be added, then

10% of (1000 + x) = 200

∴ x = 1000 gm = 1 kg

- Question 2 of 19
##### 2. Question

In a mixture of milk and water the proportion of water by weight was 75%. If in the 60 gms mixture 15 gm. water was added, what would be the percentage of water? (weight in gms.)

##### Hint

In 60 gms mixture proportion of water

=

= 45 gms

Total proportion of water in new mixture

= 45 + 15 = 60 gms.

∴ Percentage of water

=

= 80%

- Question 3 of 19
##### 3. Question

Jaydeep purchased 25 kg of rice at the rate of Rs 16.50 per kg and 35 kg of rice at the rate of Rs 24.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?

##### Hint

CP = 25 × 16.50 + 35 × 24.50 = Rs 1270

SP = 1270 ×

Price per kg

- Question 4 of 19
##### 4. Question

How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay?

##### Hint

Here, cost price of mixture

∴

and hence

- Question 5 of 19
##### 5. Question

The number of millilitres of water added to reduce 9 ml of aftershave lotion, containing 50% alcohol, to a lotion containing 30% alcohol is

##### Hint

The given solution has 50% alcohol. Water which is to be added has 0% alcohol concentration.

Alcohol concentration :

∴ Water should be added in the ratio 2 : 3

∴ Quantity of water to be added

- Question 6 of 19
##### 6. Question

An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again, it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?

##### Hint

Petrol A Petrol B I: A 0 II: III: IV: Now, amount of petrol A

=

∴ required % × l00

= 37.50%

- Question 7 of 19
##### 7. Question

Five litres of water is added to a certain quantity of pure milk costing Rs 3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture?

##### Hint

Here, S. P. of mixture = C. P. of pure milk = Rs 3 per litre

Now, S. P. of mixture

Also, C. P of water = Rs 0

By the rule of alligation :

∴ Ratio of pure milk and water in mixture

=

For five litres of water, quantity of pure milk

= 5 × 5 = 25 litres

- Question 8 of 19
##### 8. Question

Three bars of gold, weighing 6, 5, 4 and of 15, 14, 12½ carats fineness are mixed together. What is the fineness of the compound?

##### Hint

- Question 9 of 19
##### 9. Question

How many kilograms of tea powder costing Rs 31 per kg be mixed with thirty six kilograms of tea powder costing Rs 43 per kg, such that the mixture when sold at Rs 44 per kg gives profit of 10%?

##### Hint

C.P. of the mixture

=

= Rs. 40 per kg

Using alligation rule, the required ratio

=

= 1 : 3

If 3 → 36 kg, then 1 → ?

= = 12 kg.

- Question 10 of 19
##### 10. Question

A trader mixes 80 kg of tea at Rs 15 per kg with 20 kg of tea at cost price of Rs 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?

##### Hint

C.P. of mixture

∴ S.P.

- Question 11 of 19
##### 11. Question

A company blends two varieties of tea from two different tea gardens, one variety costing Rs 20 per kg and other Rs 25 per kg, in the ratio 5 : 4. He sells the blended tea at Rs 23 per kg. Find his profit percent:

##### Hint

Let the quantity of two varieties of tea be 5x kg and 4x kg, respectively.

Now, SP = 23 × 9x = 207x

and CP = 20 × 5x + 25 × 4x = 200x

Profit % =

- Question 12 of 19
##### 12. Question

In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?

##### Hint

Let C.P. of milk be Re. 1 per litre.

Then, S.P. of 1 litre of mixture = Re. 1.

Gain = 20%

∴ C.P. of 1 litre of mixture

= Rs.

By the rule of alligation, we have :

∴ Ratio of water and milk

=

- Question 13 of 19
##### 13. Question

Two liquids are mixed in the proportion of 3 : 2 and the mixture is sold at Rs 11 per kg at a 10% profit. If the first liquid costs Rs 2 more per kg than the second, what does it cost per litre?

##### Hint

C.P. of mixture

Let the cost of second liquid be Rs x.

Then, cost of first liquid be Rs (x + 2).

∴

⇒ 5x + 6 = 50 ⇒ x = Rs 8.8

∴ cost of first liquid

= Rs (8.8 + 2) = Rs 10.80

- Question 14 of 19
##### 14. Question

In what ratio must water be mixed with milk to gain 16⅔% on selling the mixture at cost price?

##### Hint

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture

= Re. 1, Gain = 50/3%

∴ C.P. of 1 litre of mixture = Re 6/7.

By the rule of alligation, we have :

∴ Ratio of water and milk

= = 1 : 6.

- Question 15 of 19
##### 15. Question

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

##### Hint

By the rule of alligation, we have :

So, ratio of 1st and 2nd quantities

= 7 : 14 = 1 : 2.

∴ Required quantity replaced = ⅔

- Question 16 of 19
##### 16. Question

How many litres of pure alcohol must be added to 10 litres of mixture which is 15% alcohol to make a mixture which will be 25% alcohol?

##### Hint

By the rule of alligation, Alcohol concentration :

∴ Alcohol must be added in the ratio of 10 : 75 or 2 : 15

∴ Quantity of alcohol to be added in 10 litres

- Question 17 of 19
##### 17. Question

How many kg of custard powder costing Rs 40 kg must be mixed with 16 kg of custard powder costing Rs 55 kg so that 25% may be gained by selling the mixture at Rs 60 kg?

##### Hint

C. P. of mixture

Let x kg be mixed. Then,

- Question 18 of 19
##### 18. Question

A butler stole wine from a butt of sherry which contained 32% of spirit and then replaced what he stole, by wine containing only 18% spirit. The butt was then of 24% strength only. How much of the butt had he stolen?

##### Hint

By the rule of alligation,

Now, wine of 32% spirit

=

∴ The rest part

i.e of the butt has been stolen.

- Question 19 of 19
##### 19. Question

A chemist has 10 litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many litres of water must he add?

##### Hint

10% of 10 litre is 1 litre.

Nitric Acid 1 ltr. Water 9 ltr. 1 ltr. is 4% of 25 litre. So final solution will have

Nitric Acid 1 ltr. Water 24 ltr. Hence 15 litres of water needs to be added.