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 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 17 :

• Theorem: If x glasses of equal size are filled with a mixture of spirit and water. The ratio of spirit and water in each glass are as follows: a1 :b1, a2, : b2, ... ax, : bx. If the contents of all the x glasses are emptied into a single vessel, ti en proportion of spirit and water in it is given by  = ( a1 + a2 + ... + ax ) : ( b1 + b2 + ... + bx ) a1 - b1 a2 - b2 ax - bx a1 - b1 a2 - b2 ax - bx

• Example :

• In three vessels each of 10 litres capacity, mixture of milk and water is filled. The ratios of milk and water are 2 : 1, 3 : 1 and 3 : 2 in the three respective vessels. If all the three vessels are emptied into a single large vessel, find the proportion of milk and water in the mixture.

• Quicker Method : Here you can use direct formula :
required ratio is  = ( 2 + 3 + 3 ) : ( 1 + 1 + 2 ) 2 + 1 3 + 1 3 + 2 2 + 1 3 + 1 3 + 2
 = ( 2 + 3 + 3 ) : ( 1 + 1 + 2 ) 3 4 5 3 4 5
 = 40 + 45 + 36 = 20 + 15 + 24 = 26 3 X 4 X 5 3 X 4 X 5
=121 : 59

Exercise :
1. Three equal glasses are filled with mixtures of milk and water. The proportion of milk and water in each glass is as follows. In the first glass as 3 : 1, in the second glassas 5 : 3 and in the third as 9 : 7. The contents of the three glasses are emptied into a single vessel. What is the proportion of milk and water in it?
2. Four vessels of equal sizes contain mixture of spirit and water. The concentration of spirit in 4 vessels are 60%, 70%, 75% and 80% respectively. If all the four mixtures are mixed, find in the resultant mixture the ratio of spirit to water.
3. Two equal glasses filled with mixtures of alcohol and water in the proportions of 2 : 1 and 1 : 1 respectively were emptied into a third glass. What is the proportion of alcohol and water in the third glass?
4. Answers : 1 = 17 : 31,   2 = 57 : 23,   3 = 7 : 5

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