8 litres are drawn from a cask full of wine and is | Alligation or Mixture Questions & Answers

Q:

Shiva purchased 280 kg of Rice at the rate of 15.60/kg and mixed it with 120 kg of rice purchased at the rate of 14.40/kg. He wants to earn a profit of Rs. 10.45 per kg by selling it. What should be the selling price of the mix per kg?

A) Rs. 22.18	B) Rs. 25.69
C) Rs. 26.94	D) Rs. 27.54

Answer & Explanation Answer: B) Rs. 25.69

Explanation:

Rate of rice of quantity 280 kg = Rs. 15.60/kg

Rate of rice of quantity 120 kg = Rs. 14.40/kg

He want to earn a profit of Rs. 10.45/kg

Rate of Mix to sell to get profit of 10.45 =

$\frac{280 x 15.60 + 120 x 14.40}{280 + 120} + 10.45 \frac{4368 + 1728}{400} + 10.45 = > 15.24 + 10.45 = 25.69$

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4 421

Q:

Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?

A) 3 : 2	B) 2 : 1
C) 1 : 2	D) 2 : 3

Answer & Explanation Answer: A) 3 : 2

Explanation:

% of milk in first bottle = 64%

% of milk in second bottle = 100 - 26 = 74%

Now, ATQ

64% 74%

68%

6 4

Hence, by using allegation method,

Required ratio = 3 : 2

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7 1329

Q:

In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?

A) 1:2	B) 3:2
C) 2:1	D) 2:3

Answer & Explanation Answer: C) 2:1

Explanation:

Given rate of wheat at cheap = Rs. 2.90/kg

Rate of wheat at cost = Rs. 3.20/kg

Mixture rate = Rs. 3/kg

Ratio of mixture =

2.90 3.20

3

(3.20 - 3 = 0.20) (3 - 2.90 = 0.10)

0.20 : 0.10 = 2:1

Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

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8 927

Q:

An alloy contains gold and silver in the ratio 5 : 8 and another alloy contains gold and silver in the ratio 5 : 3. If equal amount of both the alloys are melted together, then the ratio of gold and silver in the resulting alloy is ?

A) 113/108	B) 105/103
C) 108/115	D) 103/113

Answer & Explanation Answer: B) 105/103

Explanation:

As given equal amounts of alloys are melted, let it be 1 kg.

Required ratio of gold and silver = $\frac{\frac{5}{13} + \frac{5}{8}}{\frac{8}{13} + \frac{3}{8}} = \frac{105}{103} .$

Hence, ratio of gold and silver in the resulting alloy = 105/103.

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9 1604

Q:

A tin a mixture of two liquids A and B in the proportion 4 : 1. If 45 litres of the mixture is replaced by 45 litres of liquid B, then the ratio of the two liquids becomes 2 : 5. How much of the liquid B was there in the tin? What quantity does the tin hold?

A) 58 l	B) 65 l
C) 50 l	D) 62 l

Answer & Explanation Answer: C) 50 l

Explanation:

Let the tin contain 5x litres of liquids

$\frac{(5 x - 45) x \frac{4}{5}}{(5 x - 45) x \frac{1}{5} + 45} = \frac{2}{5}$

=> 5(4x - 36) = 2(x + 36)

=> 20x - 180 = 2x + 72

=> x = 14 litres

Hence, the initial quantity of mixture = 70l

Quantity of liquid B

= $(70 - 45) x \frac{1}{5} + 45$

= 50 litres.

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12 2493

Q:

An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?

A) 45 gm	B) 50 gm
C) 55 gm	D) 60 gm

Answer & Explanation Answer: B) 50 gm

Explanation:

Initial quantity of copper = $\frac{80}{100} x 50$ = 40 g

And that of Bronze = 50 - 40 = 10 g

Let 'p' gm of copper is added to the mixture

=> $(50 + p) x \frac{90}{100}$ = 40 + p

=> 45 + 0.9p = 40 + p

=> p = 50 g

Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.

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8 2091

Q:

A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is

A) 1 : 10	B) 10 : 1
C) 9 : 11	D) 11 : 9

Answer & Explanation Answer: A) 1 : 10

Explanation:

Customer ratio of Milk and Water is given by

Milk :: Water

6.4 0

$\frac{8}{1 + \frac{3}{8}} = \frac{64}{11}$

$\frac{64}{11}$ $\frac{64}{10} - \frac{64}{11}$

=> Milk : Water = 110 : 11 = 10 : 1

Therefore, the proportionate of Water to Milk for Customer is 1 : 10

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15 2233

Q:

In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?

A) 1:1	B) 2:1
C) 3:1	D) 1:2

Answer & Explanation Answer: A) 1:1

Explanation:

Quantity of alohol in the mixture = 40 x 5/8 = 25 lit

Quantity of water = 40 - 25 = 15 lit

According to question,

Required ratio = $\frac{20 - (40 x \frac{20}{100} x \frac{5}{8})}{15 - (40 x \frac{20}{100} x \frac{3}{8}) + 40 x \frac{20}{100}} = \frac{20}{15 - 3 + 8} = 1 : 1$

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13 3289

A) 18 litres	B) 24 litres
C) 32 litres	D) 42 litres

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally?

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