Question

Cost of pure milk is Rs.16 per litre. On adding water, the mixture is sold at Rs.15 per litre. In this way, the milkman earns 25% profit. What is the ratio of milk and water in the mixture?
(a) 25:7
(b) 7:25
(c) 15:1
(d) 1:15
(e) None of these

Answer 1

Hint: In this question, we first need to find the cost of pure milk by equating the cost of mixture to Rs.15. Then we get the actual price of the milk now as 1 litre milk is Rs.16 then by calculating how much pure milk in Rs.12 we get the ratio of the milk and the water.

Complete step-by-step answer:
Let us assume that the cost of pure milk as x.
Now, the cost of mixture can be written as the sum of the pure milk and the profit.
\[\Rightarrow \text{cost of mixture}=x+\text{25 percent of }x\text{ }\]
Given, in the question that the cost of the mixture is Rs.15
According to the percentage formula x% of y can be written as
\[\dfrac{x}{100}\times y\]
Now, we can write the equation as follows.
\[\Rightarrow x+\dfrac{25}{100}\times x=15\]
This can be further simplified as.
\[\Rightarrow \dfrac{100x+25x}{100}=15\]
Now, this can also be written as.
\[\Rightarrow \dfrac{125x}{100}=15\]
Let us now multiply with 100 on both the sides.
\[\Rightarrow 125x=15\times 100\]
Now, on dividing with 125 on both the sides we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{1500}{125} \\
 & \therefore x=Rs.12 \\
\end{align}\]
Now, given in the question that 1 litre of pure milk costs Rs.16.
Let us find the amount of milk in Rs.12.
Let us assume the amount of milk in Rs.12 as y.
Then by using the cross multiplication method we get,
\[\Rightarrow y\times 16=12\]
Now, on dividing both sides with 16 we get,
\[\begin{align}
  & \Rightarrow y=\dfrac{12}{16} \\
 & \therefore y=\dfrac{3}{4}l \\
\end{align}\]
As there is \[\dfrac{3}{4}l\] milk in the mixture then the amount of water will be:
\[\begin{align}
  & \Rightarrow 1-\dfrac{3}{4} \\
 & \Rightarrow \dfrac{1}{4}l \\
\end{align}\]
Thus, there is \[\dfrac{1}{4}l\] water in the mixture.
The ratio of milk to water is.
\[\begin{align}
  & \Rightarrow \dfrac{3}{4}:\dfrac{1}{4} \\
 & \Rightarrow 3:1 \\
\end{align}\]
Hence, the correct option is (e).

Note: It is important to note that we need to find the cost of the milk according to the cost of the mixture so that we can find the amount of milk as we already know the cost of milk per litre. We should also be careful about the calculation which should be done without neglecting any of the terms.
While finding the amount of milk that would cost Rs.12 instead of using the cross multiplication method and assuming a variable we can also directly find it by using the cost of 1 litre milk which reduces the steps. Both the methods give the same result.