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# Alligation or Mixture

1.

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

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2.

If 500 gm of salt solution has 30% salt in it, how much salt must be added to make the concentration of salt 50% in the solution?

Amount of water in solution = 100 % - 30 % = 70 % of total

Amount of water = 70 % × 500 = 350 gm

Amount of water remains same for both the solutions. Therefore, let amount of new solution be x gm.

x = 350 × (100/ 50)

x = 700

Salt added = (700 – 500) = 200 gm

Alternate solution:

Quantity of sugar to be added :

= [Solution (Required % value – Present % value)] / (100 – Required % value)

= [500 (50 – 30)] / 100 – 50

= (500 × 20) / 50

= 200 gm

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3.

Ramesh mixes 60 litres of Type-1 acid with some litres of Type-2 acid. Type-1 acid rate is Rs. 32 per litre while Type-2 rate is Rs. 23 per litre. Ramesh sells this acid-mix at rate Rs. 28 per litre. How much Type-2 acid is needed to make it a no profit no loss transaction?

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4.

One can is completely filled and contains 100% water. Another similar can is completely filled with a solution of 50% wine and 50% water. When both the cans are emptied in a steel vessel, what will be ratio of water to wine in the vessel?

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5.

Sunil started a juice (lemon syrup + water) counter. Initially he had 140 liter juice which had 30% water in it. He sold 20 liters of the juice. Then he added equal amount of lemon syrup and water. Now the ratio of water to lemon syrup became 1:2. How much water was added later on?

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6.

In what proportion must water be added to spirit to gain 20% by selling it at the cost price?

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7.

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

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8.

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 water is 16 : 65. How much wine did the cask hold originally?

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9.

Rohit buys some rice at Rs. 10.40 per kg. He mixes it with some rice having price Rs. 8.8 per kg. The final mixture becomes 15kg in weight and with total worth Rs. 146.40. What is the quantity of rice priced at Rs. 8.8 per kg?

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10.

How much milk should be added in a milk solution to make milk quantity in it 75%, if 80 L of milk solution has 45% milk in it?