Question

The average price of 80 computers in an electronic shop is Rs. 30,000 . If the highest and lowest price computers are sold out then the average price of the remaining 78 computers is Rs. 29,500 . The cost of the highest price computer is Rs. 80,000 . The cost of lowest price computer is: (a) Rs. 19,000 (b) Rs. 20,000 (c) Rs. 29,000 (d) can't be determined

Short answer

Answer: (b) Rs. 20,000.

Step-by-step solution

Calculate the total cost of 80 computers

Given that the average price of 80 computers is Rs. 30,000. We can calculate the total cost of those 80 computers. Total cost of 80 computers = Average price × Number of computers Total cost of 80 computers = Rs. 30,000 × 80

Calculate the total cost of the remaining 78 computers

Given that the average price of the remaining 78 computers is Rs. 29,500 after the highest and lowest-price computer are sold. We can calculate the total cost of those 78 computers. Total cost of 78 computers = Average price × Number of computers Total cost of 78 computers = Rs. 29,500 × 78

Calculate the cost of the lowest-price computer

Using the total cost of 80 computers, the total cost of the remaining 78 computers, and the cost of the highest-price computer, we can find the cost of the lowest-price computer. Cost of lowest-price computer = (Total cost of 80 computers) - (Total cost of 78 computers) - (Cost of highest-price computer) Substituting the values we obtained in Steps 1 and 2, and given the cost of the highest-price computer as Rs. 80,000, let's find the cost of the lowest-price computer. Cost of lowest-price computer = (Rs. 30,000 × 80) - (Rs. 29,500 × 78) - Rs. 80,000 Cost of lowest-price computer = Rs. 20,000 Hence, the cost of the lowest-price computer is Rs. 20,000. So, the correct option is (b) Rs. 20,000.

Key concepts

Average Calculation

Understanding how to calculate an average is essential for solving many math problems, especially those involving multiple items like prices of products.
In the given problem, we start with the average price of 80 computers, which is Rs. 30,000. The arithmetic mean or average is obtained by dividing the total sum by the number of items.

• Average (Arithmetic Mean) = Total Sum / Number of Items

To find the total cost of all 80 computers, we multiply their average price by the total number of computers:
\( 30,000 \times 80 = 2,400,000 \). This result represents the total cost of all the computers at the store.
Similarly, when given the average for the remaining 78 computers, we apply the same method to find their total cost:

• Total cost of 78 computers = Average price × Number of computers
• Total cost of 78 computers = Rs. 29,500 × 78

Mastering this simple calculation formula helps in breaking down larger word problems step by step.

Price Calculation

Calculating prices of items based on given conditions is an interesting aspect of word problems. In our scenario, we need to determine the price of the lowest-price computer using the information about averages and specific item prices.

• Step 1: Compute the total cost of all items using the average price.
• Step 2: Calculate the total cost for a subset with their own average price.

To solve this, we need to use the information that the highest-priced computer was sold for Rs. 80,000. The challenge then is to determine the newest total when removing this specific item and one more - the lowest-price computer.
By setting up the equation:\[\text{Cost of Lowest-Price Computer} = (\text{Total cost of 80 computers}) - (\text{Total cost of 78 computers}) - (\text{Cost of highest-price computer})\]we substitute the given values:\((30,000 \times 80) - (29,500 \times 78) - 80,000 = 20,000\).Thus, the lowest-price computer costs Rs. 20,000.
Calculations like these demand careful handling of subtraction in steps to ensure the condition meets the given criteria.

Word Problems

Word problems, like this one involving computers, often require the integration of various math concepts. These problems do not just test your ability to calculate; they also test your comprehension skills and logical thinking.
This problem involves several key steps:

• Understanding what the problem is asking for.
• Breaking it down into manageable parts (average calculations and price deduction).
• Using provided values properly to find unknowns.

These exercises improve problem-solving skills because they simulate real-life situations, such as determining costs in a shop.
Practicing with word problems hones the ability to:

• Read carefully to understand the given data and required results.
• Decide which mathematical operations to apply.
• Utilize existing formulas or derive new ones to fit the situation.

With practice, students become more comfortable with word problems, transforming complex questions into easy-to-follow steps.