An amount of ₹1,003 is to be distributed among A, B and C in the ratio of 11 : 23 : 25. How many rupees would B get more than A?
₹204
Solving the Ratio Distribution Problem
The problem asks us to distribute a total amount of ₹1,003 among three individuals, A, B, and C, according to a specific ratio of 11 : 23 : 25. We need to determine how much more money B receives compared to A.
Understanding the Ratio Distribution
A ratio like 11 : 23 : 25 means that for every 11 parts A receives, B receives 23 parts, and C receives 25 parts of the total amount. To solve this ratio distribution problem, we first need to find the total number of ratio parts.
- Ratio for A = 11 parts
- Ratio for B = 23 parts
- Ratio for C = 25 parts
Step 1: Calculate the total number of ratio parts.
The total number of parts is the sum of the individual ratio parts:
\( \text{Total Parts} = 11 + 23 + 25 \)
\( \text{Total Parts} = 59 \)
So, the total amount is divided into 59 equal parts.
Step 2: Determine the value of one ratio part.
The total amount to be distributed is ₹1,003. We divide this total amount by the total number of ratio parts (59) to find the value of a single ratio part.
\( \text{Value of one part} = \frac{\text{Total Amount}}{\text{Total Parts}} \)
\( \text{Value of one part} = \frac{1003}{59} \)
Performing the division:
\( \frac{1003}{59} = 17 \)
So, the value of one ratio part is ₹17.
Step 3: Calculate the amount received by A.
A receives 11 parts. The amount A gets is A's ratio parts multiplied by the value of one part.
\( \text{Amount A gets} = \text{Ratio for A} \times \text{Value of one part} \)
\( \text{Amount A gets} = 11 \times 17 \)
\( \text{Amount A gets} = 187 \)
A receives ₹187.
Step 4: Calculate the amount received by B.
B receives 23 parts. The amount B gets is B's ratio parts multiplied by the value of one part.
\( \text{Amount B gets} = \text{Ratio for B} \times \text{Value of one part} \)
\( \text{Amount B gets} = 23 \times 17 \)
\( \text{Amount B gets} = 391 \)
B receives ₹391.
Step 5: Calculate how many rupees B would get more than A.
To find out how much more B gets than A, we subtract the amount A gets from the amount B gets.
\( \text{Difference} = \text{Amount B gets} - \text{Amount A gets} \)
\( \text{Difference} = 391 - 187 \)
\( \text{Difference} = 204 \)
B would get ₹204 more than A.
Summary of Amounts Received
| Individual | Ratio Parts | Amount Received |
|---|---|---|
| A | 11 | \(11 \times ₹17 = ₹187\) |
| B | 23 | \(23 \times ₹17 = ₹391\) |
| C | 25 | \(25 \times ₹17 = ₹425\) |
Check: \(₹187 + ₹391 + ₹425 = ₹1003\), which matches the total amount.
Difference between B and A's share is \(₹391 - ₹187 = ₹204\).
Revision Table: Key Concepts in Ratio Distribution
| Concept | Explanation | How it applies here |
|---|---|---|
| Ratio | Compares quantities of the same kind. Written as a:b or a:b:c. | The ratio is 11:23:25 for A, B, and C. |
| Ratio Distribution | Dividing a total quantity into parts according to a given ratio. | Dividing ₹1,003 in the ratio 11:23:25. |
| Total Ratio Parts | The sum of all individual parts in the ratio. Represents the total units the quantity is divided into. | \(11 + 23 + 25 = 59\). The ₹1,003 is divided into 59 parts. |
| Value of One Part | The total quantity divided by the total ratio parts. This is the value of each unit. | \(₹1003 \div 59 = ₹17\). Each part is worth ₹17. |
| Individual Share | Calculated by multiplying the individual's ratio parts by the value of one part. | A's share = \(11 \times ₹17\), B's share = \(23 \times ₹17\), C's share = \(25 \times ₹17\). |
| Difference in Shares | The difference between the amounts received by two individuals, found by subtracting the smaller share from the larger one. | Difference between B and A = B's share - A's share. |
Additional Information on Ratio Problems
Ratio and proportion are fundamental concepts in mathematics used to compare quantities and solve problems involving division in a specific relationship. Understanding how to work with ratios is essential for various quantitative problems.
- A ratio can be simplified by dividing all parts by their greatest common divisor. In this problem, 11:23:25 is already in its simplest form as there is no common factor other than 1.
- Ratios can be used to compare more than two quantities, as seen in this problem with A, B, and C.
- Problems often require finding the value of a specific part, the total value given one part's value, or comparing different parts, like finding the difference between shares as we did here.
- Always ensure the units are consistent when working with ratios and quantities. In this case, both the total amount and the final answer are in rupees (₹).
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