# Allegation or Mixture

## Alligation

 Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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:
 A Rs. 18.50 B Rs. 19.50 C Rs. 19 D Rs. 18
Question 1 Explanation:
 Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
 A 10 B 20 C 21 D 25
Question 2 Explanation:
\begin{align} & {\text{Suppose}}\, {\text{the}}\, {\text{can}}\, {\text{initially}}\, {\text{contains}}\, \cr & 7x\, {\text{and}}\, 5x\, {\text{of}}\, {\text{mixtures}}\, {\text{A}}\, {\text{and}}\, {\text{B}}\, {\text{respectively}}. \cr & {\text{Quantity}}\, {\text{of}}\, {\text{A}}\, {\text{in}}\, {\text{mixture}}\, {\text{left}} \cr & = \left( {7x - \frac{7}{{12}} \times 9} \right)\, {\text{litres}} \cr & = \left( {7x - \frac{{21}}{4}} \right)\, {\text{litres}} \cr & {\text{Quantity}}\, {\text{of}}\, {\text{B}}\, {\text{in}}\, {\text{mixture}}\, {\text{left}} \cr & = \left( {5x - \frac{5}{{12}} \times 9} \right)\, {\text{litres}} \cr & = \left( {5x - \frac{{15}}{4}} \right)\, {\text{litres}} \cr & \therefore \frac{{\left( {7x - \frac{{21}}{4}} \right)}}{{\left( {5x - \frac{{15}}{4}} \right) + 9}} = \frac{7}{9} \cr & \Rightarrow \frac{{28x - 21}}{{20x + 21}} = \frac{7}{9} \cr & \Rightarrow 252x - 189 = 140x + 147 \cr & \Rightarrow 112x = 336 \cr & \Rightarrow x = 3 \cr\end{align}
 Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
 A Rs. 175.50 B Rs. 170 C Rs. 180 D Rs. 169.50
Question 3 Explanation:
Since first and second varieties are mixed in equal proportions.

So, their average price

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

 Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Weights of two friends Ram and Shyam are in the ratio 4:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
 A 10% B 16% C 19% D 21%
Question 4 Explanation:

Now, given ratio of Ram and Shayam's weight = 4:5

Hence, (x-15)/(15-10) = 4/5

Or, x = 19%

 Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?
 A 110 B 100 C 90 D 120
Question 5 Explanation: