Question

How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be gain of 10% by selling the mixture at Rs. 9.24 per kg.
(a) 36
(b) 42
(c) 54
(d) 63

Answer 1

Hint: Start by finding the cost price of the mixture of sugar using the data that Rs. 9.24 is 10% more than the cost price. Then let the amount of Rs. 9 sugar added to 27 kg of Rs. 7 sugar be x kg and find the total cost in terms of x. Also, the total mass of the mixture is (27+x) kg and multiply it with the cost price. Form the equation and solve to get the value of x.

Complete step-by-step answer:
We will start with the solution by letting the amount of Rs. 9 sugar mixed be x kg.
Let us start by finding the cost price of the mixture using the point that the selling price is 10% more than the cost price.
$\text{CP+ }\dfrac{10}{100}\times CP=SP$
Now it is given that the selling price is Rs. 9.24. So, if we substitute this in our equation, we get
$\dfrac{110}{100}\times CP=9.24$
$\Rightarrow CP=9.24\times \dfrac{100}{110}$
$\Rightarrow CP=9.24\times \dfrac{10}{11}$
$\Rightarrow CP=\text{Rs}\text{. }8.4$
Now the total cost of the mixture is equal to the cost price multiplied by total amount. The total amount of mixture is equal to (27+x) kg.
$\left( 27+x \right)\times 8.4=\text{ Total cost of mixture}...........\text{(i)}\text{.}$
Also, we know that the total cost of the mixture is equal to the sum of the amount of sugars used multiplied by its cost.
$\left( 27+x \right)\times 8.4=\text{ 27}\times \text{7+x}\times \text{9}$
$\Rightarrow 27\times 8.4+8.4x=\text{ 27}\times \text{7+9x}$
Now we will take all the x related terms to one side of the equation and constant terms on the other side. On doing so, we get
$27\times 8.4-\text{ 27}\times \text{7=9x-8}\text{.4x}$
$\Rightarrow 27\times 1.4=\text{0}\text{.6x}$
$\Rightarrow \dfrac{27\times 14}{6}=\text{x}$
$\Rightarrow \text{x=63kg}$
Therefore, the answer to the above question is option (d).

Note: Don’t get confused and take the 10% of the selling price while interpreting the point that the selling price is 10% more than the cost price , as you should be very clear that the percentage loss or profit are terms related to the actual pricing not to the price for which you crack the deal. The other way of thinking of this is selling price might vary from buyer to buyer depending on the bargain they put in, but the percentage should be defined from a fixed mark so that you can easily handle it. The reason that most products in the market have an MRP tag on it making it easier for all the sellers to handle their margins.