>> Aptitude >> Mixture and Allegation

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Contents:

- Aptitude
- Approximation
- Average
- Boat and Stream
- Compound interest
- Discount
- Linear Equations
- Mensuration
- Mixture and Allegation
- Number series
- Number System
- Partnership
- Percentage
- Permutation and combination
- Pipes and Cisterns
- Probability
- Problem on ages
- Profit and Loss
- Ratio and Proportions
- Simple and compound interest
- Time and Distance
- Time and work
- Trains
- Unitary Method
- Word problems
- Work and Wages

1). In what ratio must a grocer mix two types of rice costing Rs.7.50 per kg and Rs.10 per kg, respectively, so as to get a mixture worth Rs.8.25 per kg?
According to the rule of allegation, Therefore, Required ratio = 1.75 : 0.75 = 7: 3 | ||||

2). In what proportion must a grocer mix wheat at Rs.2.04 per kg and Rs.2.88 per kg so as to make a mixture of worth Rs.2.52 per kg?
According to the rule of allegation, Therefore, Required ratio = 0.36 : 0.48 = 3: 4 | ||||

3). A milkman bought 15 L of milk and mixed 3 L of water in it. If the price per kg of the mixture becomes Rs.22, what is cost price of the milk per litre?
Let CP of milk be Rs. x per kg. Then, according to the rule of allegation, Therefore, \( \Large 22 : \left(x-22\right) = 15 : 3 \) \( \Large \frac{22}{x-22} = \frac{15}{3} \) \( \Large \frac{22}{x-22} = 5 \) = 22 = 5x - 110 = 5s = 132 Therefore x = Rs.26.40 | ||||

4). A mixture of certain quantity of milk with 8 L of water is worth 45 paise per litre. If pure milk be worth 54 paise per litre, how much milk is there in the mixture?
According to the rule of allegation, Therefore, Quantity of milk = \( \Large 5 \times 8 \) = 40 L | ||||

5). The ratio of milk and water mixture of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4, respectively. In which container, is the quantity of milk relative to water minimum?
Milk in first container = g= 0.625 Milk in second container = = 0.65 Milk in third container = = 0.6 Milk in fourth container = = 0.636 So, it is clear that quantity of milk relative to water is minimum in third container. | ||||

6). A merchant has 2000 kg of rice, one part of which he sells at 36% profit and the rest at 16% profit. He gains 28% on the whole. Find the quantity sold at 16%.
According to the rule of allegation, | ||||

7). A trader has 50 kg of pulses, part of which he sells at 8% profit and rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit?
According to the rule of allegation, Part I M Part II Part I (8%) : Part II (18%) = 4 : 6 = 2 : 3 Therefore, Quantity sold at 18% = \( \Large \frac{3}{5} \times 50 \) = 30 kg | ||||

8). A person had Rs.8400. He lent a part of it at 4% and the remaining at \( \Large 2\frac{1}{3} \)% simple interest. His total annual income was Rs.294. Find the sum he lent at 4%.
SI on Rs.8400 for 1 yr = Rs.294 Therefore, Rate of interest \( \Large \frac{100 \times 294}{8400 \times 1} = \frac{7}{2} = 3\frac{1}{2} \)% According to the rule of allegation, Rate I Rate II (4%) ( 10/3%) Rate I (4%) : Rate Il (12%) = \( \Large \frac{1}{6} \) : \( \Large \frac{1}{2} \) = 1 : 3 Therefore, Money lent at 4% = \( \Large \frac{1}{4} \times 8400 \) = Rs.2100 | ||||

9). A merchant had 50 kg of pulse. He sells one part at a profit of 10% and other at 5% loss. Overall he had a gain of 7%. Find the quantity of pulses, which he sold at 10% profit and 5% loss.
According to the rule of allegation, [-ve sign indicates loss] Therefore, Ratio of pulses sold at 10% profit 5% loss = 12 : 3 = 4 : 1 Therefore, Quantity of pulse sold at 10% profit = \( \Large \frac{4}{4+1} \times 50 \) \( \Large \frac{4}{5} \times 50 \) and quantity of pulse sold at 5% loss = \( \Large \frac{1}{4+1} \times 50 \) = \( \Large \frac{4}{5} \times 50 \) = 10kg | ||||

10). A goldsmith has two qualities of gold, one of 24 carats and another of 32 carats purity. In what proportion should he mix both to make an ornament of 30 carats purity?
According to the rule of alligatic Part I Part II (24) (32) Therefore, Required ratio = Part I : Part II = 2 : 6 = 1 : 3 |