Question

Three types of rice whose rates are Rs. 38 , Rs. 43 and Rs. 49 per \(\mathrm{kg}\) are blended together to make a \(15 \mathrm{~kg}\) of new blend of rice in which there are \(8 \mathrm{kgs}, 4\) kgs 3 kgs of the respective types of rice. The average price of the new blend of rice is : (a) Rs. \(41.53\) (b) Rs. 43 (c) Rs, 40 (d) Rs. \(43.3\) Pankaj went to the post-office at the speed of \(60 \mathrm{~km} / \mathrm{hr}\) while

Short answer

Answer: (a) Rs. 41.53

Step-by-step solution

Calculate the cost of each type of rice in the blend

We are given the rates Rs. 38, Rs. 43, and Rs. 49 per kg, and their respective weights of 8 kgs, 4 kgs, and 3 kgs. So, we can calculate the cost of each type of rice in the blend: Cost of type A = Rate of A x Weight of A Cost of type B = Rate of B x Weight of B Cost of type C = Rate of C x Weight of C

Calculate the total cost of the blend

Now, we will calculate the total cost of the blend by adding the costs of each type of rice from Step 1: Total cost = Cost of type A + Cost of type B + Cost of type C

Calculate the average price of the blend

We will now calculate the average price of the blend by dividing the total cost (Step 2) by the total weight (15 kgs): Average price = Total cost / Total weight

Compare the average price with the given options

Now that we have calculated the average price in Step 3, we will compare it with the given options (a) Rs. 41.53, (b) Rs. 43, (c) Rs. 40, (d) Rs. 43.3 to determine the correct answer. Let's perform these calculations: Cost of type A = 38 x 8 = Rs. 304 Cost of type B = 43 x 4 = Rs. 172 Cost of type C = 49 x 3 = Rs. 147 Total cost = 304 + 172 + 147 = Rs. 623 Average price = 623 / 15 = Rs. 41.53 Comparing this result to the given options, the average price of the new blend of rice is (a) Rs. 41.53.

Key concepts

Blended Rice Pricing

Blended rice pricing is a method used to compute the average cost of a mixture composed of different types and quantities of rice. For example, let's consider three types of rice, each with different costs per kilogram. To find the final price of the mixed blend, we need to account for both the cost and the quantity of each rice type in the blend. - The blend's final price is influenced by the portion of each type included, resulting in a weighted contribution to the overall price. - Understanding blended rice pricing is essential to ensure fair pricing when different types of rice are mixed together. By accurately calculating this average, you can determine how much a kilogram of the blended rice should cost.

Weighted Average

Weighted average is a concept crucial for calculating the price of a product that is a combination of various other products, each contributing differently to the total. In this context, we use it to determine the cost per kilogram of a blended rice mixture. - Unlike a simple average, a weighted average considers the weight of each component differently based on its share in the total. - To calculate the weighted average, multiply each item's rate by its quantity to find its contribution to the total cost, then divide the aggregated value by the total weight. For rice, you'll consider how much each variety (contributing different weights and prices) affects the whole. This ensures a fair cost that reflects the blend's overall makeup, providing a balanced view of the cost.

Arithmetic Mean Calculation

The arithmetic mean is a fundamental concept to determine averages and is the simplest type of average most people are familiar with. For straightforward problems, it's calculated by dividing the sum of all values by the number of values. However, with items of varied weights or quantities, as in our rice blending scenario, its simple form doesn't apply directly. - The arithmetic mean becomes a weighted mean when you must consider varied quantities for each value. - It's important to understand that while the arithmetic mean offers a quick average, it does not account for proportional impact unless weighted. In blended rice pricing, converting the sum of all component costs and dividing by total weight provides the arithmetic mean, helping to deduce the per kilogram cost of the mixed product.

Unit Price Determination

Unit price determination helps customers understand the price attributed to a single unit of a product, facilitating easy comparisons and helping in cost savings. This is extremely helpful when dealing with blends of items, as it allows consumers to see the true cost per unit. - To find the unit price of a blended product, take the total cost of the blend and divide it by the total quantity. - This calculation provides a direct numerical value representing the cost for a standard unit of measurement, in this case, per kilogram. For rice lovers mixing different types for culinary purposes, understanding unit price is key to knowing how much that perfect blend will impact your budget. It’s the final per kilogram cost of your custom rice mix, adjusted for the specific varieties and weights you include.