Question

A mixture of a certain quantity of milk with 16 liters of water is worth 90P per liter.
If pure milk will be worth R.s. 1.08 per liter. How much milk is there in the mixture?
$
  {\text{A}}{\text{. 40 liters}} \\
  {\text{B}}{\text{. 50 liters}} \\
  {\text{C}}{\text{. 60 liters}} \\
  {\text{D}}{\text{. 80 liters}} \\
$

Answer 1

Hint: To solve this question we have to understand the concept of mixture and to start this question assume quantity of milk in mixture be x liter and then use the common thing that the worth of mixture is nothing but that is worth of milk.

Complete step-by-step answer:
Let the quantity of milk in the mixture be x liter.
Hence the total volume of mixture is 16+x liter.
We have a mixture of 90P per liter.
So the total price of mixture is (16+x). 90P
The worth of milk is R.S. 1.08 per liter.
Total price of milk will be R.S. (1.08).(x)
As we all know water is worthless that means we have to pay zero rupees for water.
Hence total worth of mixture is worth of milk
So,
Here all calculation is in paisa so we have written R.S 1.08= 108P
$
  \left( {16 + x} \right) \times 90 = 108 \times x \\
   \Rightarrow 1440 + 90x = 108x \\
   \Rightarrow 1440 = 18x \\
  \therefore x = 80 \\
 $
Hence option D is the correct option.

Note: Whenever we get this type of question the key concept of solving is first we have to assume what has to be found then use the data given to solve further and for this type we have to have knowledge of solving mixture problems.