Question

How many kilograms of butter worth Rs. 140 per kg must be mixed with 20 kg of butter worth Rs. 150 per kg to produce a mixture worth Rs. 144 per kg?

Answer 1

Hint: We will first let the units of butter worth 140 per kg be $x$. Then, write the total units mixed and the total cost of the butter. Find the price per kg of the mixture by dividing the total cost of the butter by the kilogram of butter mixed. Equate it to Rs. 144 and hence find the value of $x$.

Complete step-by-step answer:
We have to mix butter at the rate of Rs. 140 per kg and butter of rate Rs. 150 per kg to produce a mixture which has a rate of Rs. 144 per kg.
We have to mix 20 kg of butter worth Rs. 150 per kg and we have to find the weight of butter worth Rs. 140 per kg to produce the mixture.
Let the weight of the butter worth Rs. 140 per kg be $x$
Then, the total weight of the mixture is \[x + 20\]
Now, we will find the total cost of the mixture as,
$x\left( {140} \right) + 20\left( {150} \right) = 140x + 3000$
And the cost of the butter per kg will be $\dfrac{{140x + 3000}}{{x + 20}}$
Also, we are given that the cost of the mixture is 144 per kg
Hence, we will have the equation,
$\dfrac{{140x + 3000}}{{x + 20}} = 144$
On cross-multiplying we will get,
$140x + 3000 = 144x + 2880$
Then,
$
  3000 - 2880 = 144x - 140x \\
   \Rightarrow 120 = 4x \\
$
On dividing the equation throughout by 4, we will have,
$x = 30$
Hence, we have to take 30kg of butter worth 140 per kg.

Note: The total cost of the mixture is the sum of the product of the price of each type of butter with the units of the butter. Also, to find the cost per kg, we will divide the total cost by total units. Avoid calculation mistakes while solving for the value of $x$.