Ratio of salary of A & B is 5:7. If A gets ₹2500, what does B get?

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Solving Salary Ratios: A Step-by-Step Guide (With Examples!)

Understanding ratios is a crucial skill, especially when dealing with money! Ratios help us compare quantities and make smart decisions about our finances. Imagine you're comparing salaries – that's where ratios come in handy. This guide will show you how to solve a common salary ratio problem: "If the ratio of A's salary to B's salary is 5:7, and A earns a certain amount, how do we calculate B's salary?" Let's dive in!

Understanding the Salary Ratio: 5:7

Let's break down what a ratio like 5:7 means. In our example, it means that for every ₹5 A earns, B earns ₹7. It's all about the proportion. It doesn't mean A earns exactly ₹5 and B earns exactly ₹7. It shows their earnings relationship.

We know the ratio of A to B's salary is 5:7. This will help us find out B's salary once we have A's.

Step-by-Step Solution: Finding B's Salary

Here’s how to solve the problem step-by-step. Don't worry; it's easier than it looks!

Step 1: Identify the Given Information

First, let's gather what we know:

• Ratio of A:B = 5:7
• A's Salary = ₹2500

Step 2: Set up the Proportion

Now, we'll put the ratio and the known information into a proportion. A proportion is just two ratios set equal to each other.

So, we'll write it as: (A's Salary) / (B's Salary) = 5 / 7 or ₹2500 / (B's Salary) = 5 / 7

Step 3: Solve for B's Salary

To find B's salary, we'll use a method called cross-multiplication. Here's how it works:

1. Multiply the numerator (top number) of the first ratio by the denominator (bottom number) of the second ratio: 5 * B's Salary
2. Multiply the denominator (bottom number) of the first ratio by the numerator (top number) of the second ratio: 7 * ₹2500
3. Set the two results equal to each other: 5 * B's Salary = 7 * ₹2500
4. Isolate B's Salary by dividing both sides of the equation by 5: B's Salary = (7 * ₹2500) / 5

Step 4: Calculate the Answer

Now, let's do the math!

B's Salary = (7 * ₹2500) / 5

B's Salary = ₹17500 / 5

B's Salary = ₹3500

Step 5: Verify the Answer

Does our answer make sense? Let's check. We calculated B's salary as ₹3500. Let's see if it keeps the 5:7 ratio.

A's Salary : B's Salary = 2500 : 3500

Divide both by 500:

5 : 7

Yes! Our answer is correct.

Example Problems

Let's practice with a new example:

Problem 1: If the ratio of X's salary to Y's salary is 3:4, and X earns ₹3000, what does Y earn?

Solution:

1. Set up the proportion: ₹3000 / (Y's Salary) = 3 / 4
2. Cross-multiply: 3 * Y's Salary = 4 * ₹3000
3. Solve for Y's Salary: Y's Salary = (4 * ₹3000) / 3 = ₹4000

Problem 2: The ratio of two salaries is 2:9. If the lower salary is ₹1000, what is the higher salary?

Solution:

1. Set up the proportion: ₹1000 / (Higher Salary) = 2 / 9
2. Cross-multiply: 2 * Higher Salary = 9 * ₹1000
3. Solve for Higher Salary: Higher Salary = (9 * ₹1000) / 2 = ₹4500

Key Takeaways

• Understand the Ratio: Ratios express the relationship between two or more quantities.
• Set up the Proportion: Write the ratio and the given information as a proportion.
• Cross-Multiply: This is your key to solving for the unknown variable.
• Calculate and Verify: Always check if your answer makes sense in the context of the problem.

Understanding ratios is a valuable skill that goes beyond just salary comparisons. It applies to budgeting, investment, and many other financial decisions!

Conclusion

You've learned how to solve salary ratio problems! We took a problem and broke it down into easy steps. Remember, the ratio 5:7 doesn't mean exact amounts, but it expresses a proportional relationship. You can now confidently tackle these problems and apply this knowledge to other real-world situations.

Practice makes perfect! Try solving more ratio problems to strengthen your understanding. Happy calculating!

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