Question:

A trader mixes 26 kg of rice at Rs.20 per kg with 30 kg of rice of other variety at Rs.36 per kg and sells the mixture at Rs.30 per kg. His profit percent is

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You can also solve this using the weighted average cost price: \(\frac{26 \times 20 + 30 \times 36}{56} = \frac{1600}{56} \approx 28.57\). Comparing this unit CP with the unit SP of \(30\) yields the same profit margin, but working with total values avoids messy fractions.
Updated On: May 9, 2026
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The Correct Option is B

Solution and Explanation



Step 1: Understanding the Question:

We are given the quantities and unit prices of two types of rice that are mixed together. We need to find the overall profit percentage after selling the entire mixture at a given rate.


Step 2: Key Formula or Approach:

First, calculate the total Cost Price (CP) and the total Selling Price (SP).
\(\text{Profit} = \text{Total SP} - \text{Total CP}\).
\(\text{Profit %} = \left(\frac{\text{Profit}}{\text{Total CP}}\right) \times 100\).


Step 3: Detailed Explanation:

Let's find the total Cost Price (CP) of the mixture.
Cost of \(26\) kg rice at Rs. \(20\)/kg = \(26 \times 20 = 520\) Rs.
Cost of \(30\) kg rice at Rs. \(36\)/kg = \(30 \times 36 = 1080\) Rs.
Total CP of the mixture = \(520 + 1080 = 1600\) Rs.
Total weight of the mixture = \(26 + 30 = 56\) kg.
The trader sells the entire mixture at Rs. \(30\) per kg.
Total Selling Price (SP) = \(56 \times 30 = 1680\) Rs.
Now, calculate the profit: \[ \text{Profit} = \text{Total SP} - \text{Total CP} = 1680 - 1600 = 80 \text{ Rs.} \] Finally, calculate the profit percentage: \[ \text{Profit %} = \left( \frac{80}{1600} \right) \times 100% \] \[ \text{Profit %} = \frac{1}{20} \times 100% = 5% \]

Step 4: Final Answer:

His profit percent is \(5%\).
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