Sample Material of Online Coaching For SSC CGL (Tier - 2) - Alligation or Mixture
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter: Alligation or Mixture)
It is the rule that is used to determine the mean value of the mixture when the prices of the individual items being mixed together and the proportion in which they are being mixed are given. Here, the value of the mixture is always higher than the lowest value and lower than the higher value of the items being mixed.
According to the Rule of Alligation
Quantity of cheaper = Price of dearer - Mean price Quantity of dearer Mean price - Price of cheaper
It can be also expressed as,
therefore, (Cheaper quantity : Dearer quantity) = (y – m) : (m – x)
Where, mean price (m) is the cost price of a unit quantity of the mixture.
Also, if a container contains x units of liquid from which y units are taken out
and replaced by water. After n operations, the quantity of pure liquid is [x(1 -
y/x)n] unit.
Example 1: How many kilograms of rice costing Rs 18 per kg must be mixed with 30 kg of rice costing Rs 14 per kg, so that the resultant mixture cost Rs 15 per kg.
Solution. Applying the rule of alligation, we have
therefore = Quantity of cheaper rice = 3 Quantity of dearer rice 1
If cheaper rice is 3 kg, dearer rice is 1 kg.
If cheaper rice is 30 kg, dearer rice = (30 x 1) kg = 10 kg 3
Example 2: In what proportion must a person mix rice Rs 12.00 per kg and Rs 14.40 per kg so as to make a mixture worth Rs 12.60 per kg?
Solution.
By the alligation rule,
Quantity of cheaper rice = 180 = 3 Quantity of dearer rice 60 1
therefore, He must mix rice in the ratio 3 : 1.
:: Home Assignment for Practice ::
1. In what ratio, tea at Rs 90 per kg should be mixed with another tea at Rs 120 per kg to get a tea of Rs 100 per kg
(a) 2 : 1
(b) 3 : 1
(c) 3 : 2
(d) 4 : 3
2. Two varieties of rice at Rs 10 per kg and Rs 12 per kg are mixed together in the ratio 1 : 2. Find the average price of the resulting mixture
(a) Rs 11 per kg
(b) Rs 11.22 per kg
(c) Rs 11.33 per kg
(d) Rs 11.44 per kg
3. On combining two groups of students having 30 and 40 marks respectively in an exam, the resultant group has an average score of 34. Find the ratio of the number of students in the first group to the number of students in the second group.
(a) 2 : 1
(b) 3 : 2
(c) 3 : 1
(d) 4 : 3
4. On mixing two classes of students having average marks 25 and 40 respectively, the overall average obtained is 30 marks. Find the number of students in first class if the second class has 30 students.
(a) 45
(b) 60
(c) 70
(d) 80
5. 4 kg of rice at Rs 5 kg is mixed with 8 kg of rice at Rs 6 per kg. Find the average price of the mixture
(a) Rs 5 per kg
(b) Rs 5.55 per kg
(c) Rs 5.66 per kg
(d) Rs 6 per kg