If an amount of Rs. 990 is divided among A, B and C in the ratio of 3 : 4 : 2, then B will get:
Rs. 440
Calculating Shares When Dividing an Amount in a Ratio
The question asks us to divide a total amount of Rs. 990 among three individuals, A, B, and C, according to a specific ratio, which is 3 : 4 : 2. We need to find the share that B receives from this division.
When an amount is divided in a given ratio, the total number of parts in the ratio represents the total number of equal portions the amount is divided into. The individual shares are determined by their respective parts in the ratio multiplied by the value of one part.
Steps to Divide the Amount According to the Ratio
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Find the total number of ratio parts: Add the individual parts of the ratio together.
The given ratio for A : B : C is \(3 : 4 : 2\).
Total ratio parts = \(3 + 4 + 2 = 9\)
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Calculate the value of one ratio part: Divide the total amount by the total number of ratio parts.
Total amount to be divided = Rs. 990
Total ratio parts = 9
\(\text{Value of one part} = \frac{\text{Total amount}}{\text{Total parts}} = \frac{990}{9}\)
\(\text{Value of one part} = 110\)
So, each ratio part is worth Rs. 110.
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Calculate B's share: Multiply the value of one part by B's ratio part.
B's ratio part = 4
Value of one part = Rs. 110
\(\text{B's share} = \text{B's ratio part} \times \text{Value of one part}\)
\(\text{B's share} = 4 \times 110\)
\(\text{B's share} = 440\)
Therefore, B will get Rs. 440 from the total amount of Rs. 990.
We can also calculate the shares of A and C for completeness:
- A's share = A's ratio part \(\times\) Value of one part = \(3 \times 110 = 330\). A gets Rs. 330.
- C's share = C's ratio part \(\times\) Value of one part = \(2 \times 110 = 220\). C gets Rs. 220.
To verify, the sum of the shares should equal the total amount: \(330 + 440 + 220 = 990\). This matches the total amount given.
Revision Table: Ratio Division Key Concepts
| Concept | Description | Formula/Method |
|---|---|---|
| Ratio | Comparison of two or more quantities of the same kind. | a : b or a : b : c |
| Sum of Ratio Parts | Total number of equal divisions of the whole amount. | Add all parts of the ratio. |
| Value of One Part | The amount corresponding to a single unit of the ratio. | Total Amount / Sum of Ratio Parts |
| Individual Share | The amount received by one person. | Individual Ratio Part × Value of One Part |
Additional Information: Applications of Ratio Division
Dividing quantities in a specific ratio is a fundamental concept with many real-world applications. Understanding ratio division is crucial for various problems.
- Business and Finance: Dividing profits among partners based on investment ratio, allocating budgets.
- Mixtures: Determining the quantity of ingredients needed in a recipe or a chemical mixture based on a given ratio.
- Geometry: Dividing a line segment in a given ratio, scaling drawings.
- Resource Allocation: Distributing resources, tasks, or rewards according to specific criteria or proportions.
Mastering ratio division helps in solving problems involving proportional distribution and comparison of quantities.
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