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 (₹).
Important Questions from Quant Based Puzzle
Three years ago, the difference between the age of Ravish and the age of Kailash was 18 years. Three years from today, Ravish will be three times as old as Kailash. What is the present age of Ravish (in years)?
Seven years from now, Anamika will be as old as Malini was 4 years ago. Srinidhi was born 2 years ago. The average age of Anamika, Malini and Srinidhi 10 years from now will be 33 years. What is the present age of Anamika?
In an exam of 80 questions, a correct answer gives 1 marks but a wrong answer deducts 1 marks, and if a question in not attempted there is no deduction in marks. If a student attempted only 80% of the question and got 32 marks, then how many questions did he answer correctly?
The ratio of the present ages of Asha and Lata is 5 : 6. If the difference between their ages is 6 years, then what will be Lata’s age after 5 years?
Five years ago, the ratio of the ages of Tarun and Saurabh was 4 ∶ 1. After five years, the ratio of their ages will be 2 ∶ 1. What is the present age (in years) of Saurabh?
