Shortcut – Mixtures and Allegation

Finding average price of a mixture.

Ap = Average price of the mixture.
A1 = Price of the first variety.
A2 = Price of the second variety.
N1 = Quantity of the first variety.
N2 = quantity of the second variety.

Question:

Two varieties of rice with prices Rs. 30 per kg and Rs. 40 per kg are mixed in the ratio 2 : 3. Find the mean price.

Answer:

N1 = 2;
N2 = 3
A1 = 30;
A2 = 40
Substitute the values in the above equation.
Mean price = Rs. 36

Shortcut – Mixtures and Allegation

Allegation Rule.

Question:

In what ratio two varieties of rice worth Rs. 40 per kg and Rs. 60 per kg should be mixed to give a variety worth Rs. 46 per kg?

Answer:

The two mixtures have to be mixed in the ratio 7 : 3 to get Rs. 46 mixture.

Shortcut – Mixtures and Allegation

Successive removal and replacement type. F=I[1-(R/I)]^{N}
I – Initial quantity;
R – Removal quantity;
F – Final quantity;
N – Number of processes.

Question:

A container has 1000 liters of wine. 100 liters of wine is drawn from the container and filled with water. This process is done two more times. What is the ratio between wine and water in the final mixture?

Answer:

Number of draws n = 3
$FQ = 1000 [1-(100/1000)]^{3} = 1000(0.9)^{3} = 729$
Present quantity of wine = 729
Present quantity of water = 1000 – 729 = 271
Ratio between wine and water = 729 : 271
(Or)
729 = final quantity of wine.

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