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Alligation or Mixture problems

1. Tea worth of Rs. 135/kg and Rs. 126/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____?
Options
A. Rs. 169.50
B. Rs.1700
C. Rs. 175.50
D. Rs. 180

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Correct Answer: Rs. 175.50

Explanation:

To solve the problem, let's define the prices and quantities of the different varieties of tea being mixed.

Given:

Price of the first variety of tea = Rs. 135/kg
Price of the second variety of tea = Rs. 126/kg
Ratio of the first, second, and third varieties = 1 : 1 : 2

Let the price of the third variety of tea be $x$ Rs./kg.

The total mixture is worth Rs. 153/kg. Since the ratio of the tea varieties is 1:1:2, we can assume the quantities of each type of tea in the mixture to be:

Quantity of the first variety = 1 unit
Quantity of the second variety = 1 unit
Quantity of the third variety = 2 units

The total cost of the mixture can be expressed as the weighted average cost of the individual varieties based on their respective quantities.

Let's compute the cost per unit for the mixture:

\text{Total cost} = (1 \text{ unit} \times 135 \text{ Rs./kg}) + (1 \text{ unit} \times 126 \text{ Rs./kg}) + (2 \text{ units} \times x \text{ Rs./kg})

The total quantity of the mixture is:

1 \text{ unit} + 1 \text{ unit} + 2 \text{ units} = 4 \text{ units}

The average price per kg of the mixture is given as Rs. 153. Therefore, we set up the equation:

\frac{135 + 126 + 2x}{4} = 153

First, simplify the numerator:

135 + 126 + 2x = 261 + 2x

Next, substitute this back into the equation and solve for $x$ :

\frac{261 + 2x}{4} = 153

Multiply both sides by 4 to clear the denominator:

261 + 2x = 612

Now, isolate $x$ :

2x = 612 - 261

2x = 351

x = \frac{351}{2}

x = 175.5

Thus, the price of the third variety of tea is Rs. 175.50 per kg.

2. A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Options
A. 1/3
B. 1/4
C. 1/5
D. 1/7

4. The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?
Options
A. 25
B. 21
C. 12
D. 24

5. A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options
A. 10 liters
B. 20 liters
C. 30 liters
D. 40 liters

6. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg?
Options
A. 36 Kg
B. 42 Kg
C. 54 Kg
D. 63 Kg

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
Options
A. Rs. 19.50
B. Rs. 19
C. Rs. 18
D. Rs. 18.50

8. The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture?
Options
A. 4
B. 5
C. 8
D. None of these

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9. The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:
Options
A. 25
B. 30
C. 45
D. cannot be determined

Correct Answer: 30

Explanation:

pool : kerosene

3 : 2(initially)

2 : 3(after replacement)

$\frac{R e m a i n i n g Q u a n t i t y}{I n i t i a l Q u a n t i t y} = (1 - \frac{R e p l a c e d Q u a n t i t y}{T o t a l Q u a n t i t y})$

(for petrol) $\frac{2}{3} = (1 - \frac{10}{k})$

=> K = 30

Therefore the total quantity of the mixture in the container is 30 liters.

10. A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :
Options
A. 83.33 ml
B. 90.90 ml
C. 99.09 ml
D. can't be determined

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