How much quantity of rice of the price 18 rupees per kg should be mixed with 45 kg of rice having price 26 rupees per kg so that after selling mixture at 25.2 rupees per kg there is a profit of 5%?a)30 kgb)25 kgc)20 kgd)15 kge)None of theseCorrect answer is option 'D'. Can you explain this answer?

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Answer

To solve this problem, we need to find the quantity of rice that should be mixed in order to achieve a profit of 5% when selling the mixture at 25.2 rupees per kg.

Let's assume that x kg of rice of the price 18 rupees per kg should be mixed.

Selling Price and Profit Percentage:
The selling price of the mixture is given as 25.2 rupees per kg, and we want to have a profit of 5%.

Profit percentage is calculated as:
Profit Percentage = (Profit / Cost Price) * 100

In this case, the profit percentage is given as 5%. So, we have:
5 = (Profit / Cost Price) * 100

We can rearrange this equation to find the profit:
Profit = (5/100) * Cost Price

Cost Price of the Mixture:
The cost price of the mixture is the weighted average of the cost prices of the two types of rice being mixed.

Cost Price = (Cost Price of Rice 1 * Quantity of Rice 1 + Cost Price of Rice 2 * Quantity of Rice 2) / Total Quantity

In this case, the cost price of rice 1 is 18 rupees per kg, the quantity of rice 1 is x kg, the cost price of rice 2 is 26 rupees per kg, and the quantity of rice 2 is 45 kg.

So, we have:
Cost Price = (18x + 26 * 45) / (x + 45)

Solving the Equation:
Now, let's substitute the profit and cost price equations into the profit percentage equation:

(5/100) * Cost Price = (Profit / Cost Price) * 100

(5/100) * [(18x + 26 * 45) / (x + 45)] = [(5/100) * (18x + 26 * 45)] / (18x + 26 * 45) * 100

Simplifying this equation, we get:
5 * (18x + 26 * 45) = 5 * (18x + 26 * 45)

This equation simplifies to:
90x + 130 * 45 = 90x + 130 * 45

The x term cancels out, and we are left with:
130 * 45 = 130 * 45

Since the equation is true for any value of x, it means that any quantity of rice can be mixed to achieve a profit of 5%. Therefore, the answer is None of these (Option E).

Note: The given information in the question is not sufficient to determine the quantity of rice that should be mixed to achieve the desired profit.

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