Disclaimer: All the Information provided in this post are prepared & compiled by A. Praveen Kumar, SPM, Papannapet SO502303, Telangana State for in good faith of Postal Assistant Exam Aspirants. Author of blog does not accepts any responsibility in relation to the accuracy, completeness, usefulness or otherwise, of contents.
ALLIGATION AND MIXTURES
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 Alligation:
It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.
 Mean Price:
The cost of a unit quantity of the mixture is called the mean price.
 Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid =

x

1 

y

n

units.
 
x

4.

Rule of Alligation:

If two ingredients are mixed, then

Quantity of cheaper

=

C.P. of dearer  Mean Price
 
Quantity of dearer

Mean price  C.P. of cheaper

 
(Cheaper quantity) : (Dearer quantity) =

1. In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre?
2. In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg?
3. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Sol: ratio of first and second part = 4 : 6 = 2 : 3
Quantity of 2 kind = (1000*3/5) = 600 Kg
4.A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is
Sol: Total interest of rs 4000 in 1 year = 52
Average rate = (352 * 100) / 4000 * 1 = 8.8% by rule of allegation (8  8.8) : (108.8) = 1.2 : 0.8 = 3:2 part one = (4000*3/5) = 2400
5.729 ml of mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7 : 3
Sol: 729 * 7/9 = 567 ml, Water = 729  567 = 162
Let water added is x ml 567/(162 + x) = 7/3 or 1701 = 1134 + 7x or x = 81 ml
6.A sum of Rs. 312 was divided among 100 boys and girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls is
Sol: 312  240 : 360  312 = 3 : 2
Number of girl = 100*2/5 = 40
7.A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage uf alcohol was found to be 26%. The quantity of whisky replaced is
Sol: Ratio of first and second = 7 : 14 = 1 : 2
Required quantity 2/3
8.A man covered a distance of 2000 km in 18 hours partly by bus at72 kmph and partly by train at 160 kmph. The distance covered by bus is
Sol: Average distance traveled = 1000/9
72  1000/9 : 160  1000/9 = 440/9 : 352/9 =5 : 4 distance traveled by bus = 18*5/9 = 10 distance traveled by bus in 10 hrs = 72 * 10 = 720 
9. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
 
 
10. 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
 
 
11. In what ratio must water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre?
 
 
12.In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be worth Rs. 64.50 per Kg?
 
Sol : By the rule of alligation:
Cost of 1 Kg tea of 1st kind cost of 1 kg tea of 2nd kind
Required ratio is = 750: 250= 3:1
 
13. Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
 
Sol:
 
Required ratio = 60 : 90 = 2 :3
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