Calculating Share in a Given Ratio

This question asks us to divide a certain amount of money (Rs. 126) among three people (A, B, and C) according to a specified ratio (3 : 2 : 5) and find out how much money C will receive.

Understanding Ratio Division

When an amount is divided in a ratio, it means the total amount is split into parts proportional to the numbers in the ratio. The sum of the numbers in the ratio represents the total number of equal parts the amount is divided into.

Steps to Solve the Problem

Here are the steps to find the amount C gets:

1. Find the total number of parts in the ratio.
2. Determine the value of one part by dividing the total amount by the total number of parts.
3. Calculate the share of each person by multiplying their respective ratio part by the value of one part.

Applying the Steps to the Problem

• The given ratio for the division of money among A, B, and C is 3 : 2 : 5.
• The total amount of money to be divided is Rs. 126.

Step 1: Find the total number of parts.

The total number of parts is the sum of the individual ratio parts:

\(\text{Total parts} = 3 + 2 + 5 = 10\)

So, the total amount is divided into 10 equal parts.

Step 2: Determine the value of one part.

The value of one part is calculated by dividing the total amount by the total number of parts:

\(\text{Value of one part} = \frac{\text{Total amount}}{\text{Total parts}} = \frac{126}{10}\)

\(\text{Value of one part} = 12.6\)

So, each part is equal to Rs. 12.6.

Step 3: Calculate the share of C.

C's share corresponds to 5 parts of the ratio. To find C's share, multiply the value of one part by C's ratio part:

\(\text{C's share} = \text{C's ratio part} \times \text{Value of one part}\)

\(\text{C's share} = 5 \times 12.6\)

\(\text{C's share} = 63\)

Therefore, C will get Rs. 63.

We can also calculate the shares of A and B for completeness:

• A's share = A's ratio part × Value of one part = \(3 \times 12.6 = 37.8\)
• B's share = B's ratio part × Value of one part = \(2 \times 12.6 = 25.2\)

Let's check if the total shares add up to the total amount:

\(\text{Total amount} = \text{A's share} + \text{B's share} + \text{C's share}\)

\(\text{Total amount} = 37.8 + 25.2 + 63 = 63 + 63 = 126\)

The total shares add up to Rs. 126, confirming our calculations are correct.

Summary of Shares

The amount of money C will get is Rs. 63.

Revision Table: Key Concepts in Ratio Division

Additional Information: Applications of Ratio

Ratios are used in many real-life situations and various fields of study. Understanding how to work with ratios is fundamental. Some common applications include:

• Mixing Ingredients: Recipes often use ratios to specify the proportions of different ingredients.
• Scaling Maps and Models: Ratios are used to represent the relationship between distances on a map or model and the actual distances. For example, a scale of 1:100 means 1 unit on the map represents 100 units in reality.
• Sharing Quantities: Dividing profits, expenses, or goods among individuals or groups based on agreed-upon ratios.
• Comparing Quantities: Ratios provide a simple way to compare different quantities.
• Science and Engineering: Ratios are used in calculations involving concentrations, proportions of elements in compounds, gear ratios, etc.

Ratio and proportion problems are common in aptitude tests and everyday calculations involving sharing and scaling.