Question

A has 50 coins of 10 paise denominations. While \(B\) has 10 coins of 50 paise denominations. \(C\) has 20 coins of 25 paise denominations while \(D\) has 25 coins of 20 paise denominations. The average number of paise per person is : (a) 450 paise (b) 500 paise (c) 600 paise (d) can't be determined

Short answer

Answer: (b) 500 paise

Step-by-step solution

Calculate Total Number of Paise for Each Person

To find the total number of paise for each person, multiply the number of coins they have by the denomination of the coins. For A: 50 coins * 10 paise = 500 paise For B: 10 coins * 50 paise = 500 paise For C: 20 coins * 25 paise = 500 paise For D: 25 coins * 20 paise = 500 paise

Calculate the Total Number of Paise for All Four People

To find the total number of paise for all four people, add up the total number of paise for each person. Total paise = paise of A + paise of B + paise of C + paise of D Total paise = 500 paise + 500 paise + 500 paise + 500 paise Total paise = 2000 paise

Calculate the Average Number of Paise per Person

To find the average, divide the total number of paise for all four people by the number of people, which is 4. Average paise per person = Total paise / 4 Average paise per person = 2000 paise / 4 Average paise per person = 500 paise

Identify the Correct Option

Now that we’ve calculated the average number of paise per person, we can identify the correct option. The correct option is: (b) 500 paise

Key concepts

Coin Denominations

When we talk about coin denominations, we refer to the various values that coins can have. Each person in the given problem has coins of different denominations, meaning that they have coins worth different amounts of paise. For example, A has 50 coins, each worth 10 paise. This means the total value of A's coins is calculated by multiplying the number of coins by the denomination, such as 50 coins times 10 paise. This gives a total of 500 paise for A's collection. Similarly, B, C, and D have their coins, each in distinct denominations. Understanding the concept of coin denominations is essential before you solve problems involving money or currencies, as it allows you to determine the total monetary value of a set of coins. Coin denominations simplify the calculation of total values, which is a skill utilized heavily in financial calculations and everyday transactions.

• Coin denomination refers to the face value of a coin.
• Combining the number of coins with their denomination helps in finding the total monetary value.
• Different denominations are fundamental in currency systems worldwide.

Mathematical Problem Solving

Mathematical problem solving is about understanding how to approach and work through math-related challenges using logical reasoning and analytical skills. In the problem provided, each step involves straightforward calculations that require identifying what needs to be done and applying the correct mathematical methods. Begin by recognizing the requirement to calculate individual paise values for different people. This involves multiplying the number of coins by their denomination. Afterwards, you must aggregate the total paise count for all individuals combined. This problem-solving approach necessitates adding the individual values together to form a cumulative sum. Finally, the problem asks you to calculate the average paise per person. For this, you'll need to use division to determine the average value. Mathematical problem solving involves breaking down a problem into manageable parts and solving each part methodically to find the solution.

• Understand the problem fully before beginning calculation.
• Break down the problem into smaller, manageable pieces.
• Apply logical steps to reach the solution, at each phase.

Arithmetic Operations

Arithmetic operations are the fundamental building blocks of mathematics, involving basic calculations such as addition, subtraction, multiplication, and division. In this exercise, you primarily employ multiplication and division to resolve the task at hand. Each person's total value of coins in paise is calculated using multiplication. This means you multiply the number of coins by the denomination value, for example, A having 50 coins each worth 10 paise results in 500 paise. Once we calculate the total paise for each person, these values are added together, showcasing the use of addition. The sum of all paise amounts is used to find the average by employing division: the total sum divided by the number of people gives the average value, which is 500 paise in this case. Arithmetic operations are simple yet powerful tools that provide us with the means to execute such calculations accurately.

• Multiplication to find total value of coins.
• Addition to sum together all individual totals.
• Division to compute an average, distributing total equally.