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

Direct Formula / Rule 2 :

• Theorem: The quantity of salt at Rs x per kg that a man must mix with n kg of salt at Rs y per kg, so that he may, on selling the mixture at Rs z per kg, gain p% on the outlay is given by

= [ 100z - y(100 + p)/x(100 + p) - 100z ] X n

Note : if we suppose that the quantity of salt at Rs x be m, then we have.

• Example :

• How many kg of salt at 42 P per kg must a man mix with 25 kg of salt at 24 P per kg, so that he may, on selling the mixture at 40 per kg, gain 25% on the outlay?

• Detail Method : Let the required amount of salt be x kg
As per Question,
Because Selling price of the mixture = 40 per kg given
so Cost price,of the mixture = 40 X 100/125 X (x + 25)
or, 42x + 24 x 25 = 32x + 32 x 25
or, 10x = 25 x 8
so x = 20 kg.

• Ailigation Method :
Cost price,of the mixture = 40 + 100/125 P = 32 p per kg..
By the rule of fraction :  42 Mean price     32 24 8 10
Ratio = 4 : 5
Thus for every 5 kg of salt at 24 P, 4 kg of salt at 42 P is used.
the required no. of kg = 25 x 4/5 = 20

• Quicker Method : Here you can use direct formula :

= [ 100z - y(100 + p)/x(100 + p) - 100z ] X n

= [ 100 x 40 - 24(100 + 25)/42 x (100 + 25) - 100 x 40 ] X 25

= [ 4000 - 3000/5250 - 4000 ] X 25

= [ 1000/1250 ] X 25 = 20 kg.

Exercise :
1. Jaydeep purchased 25 kg of rice at the rate of Rs 16.50 per kg and 35 kg ofrice at the rate of Rs 25.50 per kg. He mixed the two and sold the mixture. Approximately, at What price per kg did he sell the mixture to make 25 per cent profit?   [Hint : here you need to find z as per formula]

2. Jagtar purchases 30 kg of wheat at the rate of Rs 11.50 per kg and 20 kg ofwheat at the rate of Rs 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 per cent profit?   [Hint : here you need to find z as per formula]

3. In what proportion must a grocer mix one kind of wheat at Rs 4.50 per kg with another at Rs 4 per kg in order that by selling the mixture at Rs 5.20 per kg he may make a profit of 20 per cent?

4. Answers : 1 = Rs 26.50,   2 = Rs 16.30,   3 = 2 : 1

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