Income & Expenditure: A's Financial Puzzle Solved!

Hey guys! Let's dive into a fun math problem about income, expenditure, and savings. We're going to break down how A's spending habits change when his income gets a boost. It's like a real-life financial scenario, so pay close attention! This is a fantastic exercise in understanding percentages and how they relate to our money. So, grab a coffee, sit back, and let's solve this puzzle together. We'll break down everything step-by-step, making sure it's super easy to follow. The key here is to understand how changes in income affect spending and saving. By the end of this, you'll have a much clearer picture of personal finance basics!

Understanding the Basics: Income, Expenditure, and Savings

Alright, before we jump into the problem, let's make sure we're all on the same page with the basics. Income is simply the amount of money A earns each month. Think of it as the total amount coming in. Expenditure is the money A spends. It's what goes out to cover all the things A needs and wants, like food, housing, entertainment, and everything else. And finally, savings is the money A doesn't spend. It's what A puts aside for future goals or a rainy day. These three things are super important, right? These three things are all related; Your income minus your expenditure will equal your savings. The goal here is to learn how they affect each other. This problem uses percentages, which might seem scary at first, but they're actually super useful for comparing and understanding changes in different amounts, like how much more A spends when A gets more money.

Let's look at the first part of the problem. A spends 68% of his monthly income. This means that for every 100 rupees A earns, A spends 68 rupees. The remaining 32 rupees (100 - 68) are saved. This initial setup is important because it sets the baseline. It tells us how A is managing their money before any changes occur. So, you now know what each piece of the puzzle means, and we can move on to the next part. That is how A's income changes, and how that affects their spending and savings. Let's see how that works. The cool thing about percentages is that they let us scale the income up or down and then compare them. This helps us understand if there is a difference. Ready to crunch some numbers? Let's get started.

Setting Up the Initial Scenario

To solve this problem, let's start by assuming A's initial monthly income is 100 units (it could be dollars, rupees, or any currency; the unit doesn't matter for percentage calculations). The starting point is setting up the basic scenario.

• Initial Income: 100 units
• Expenditure: 68% of 100 = 68 units
• Savings: 32% of 100 = 32 units

This initial setup is our baseline. It tells us how A manages his money before any changes happen. Now we know that the expenditure is 68% and the savings is 32%. This makes it easy to calculate everything else.

The Income Boost: What Happens When A Earns More?

Now, the problem tells us that A's monthly income increases by 25%. This is a good thing! Let's figure out how this impacts A's finances. You know the initial setup, and now comes a change! We need to find the new values.

• New Income: 100 + 25% of 100 = 100 + 25 = 125 units

So, A's income increases from 100 units to 125 units. You need to remember that the initial income of 100 units serves as a base. When the percentage is calculated, the result of that percentage should be added to the initial value to arrive at the new value. See how a little more income affects everything else. Now we'll look at how the savings and expenditure change.

The Savings Increase: Impact on the Financials

The problem also states that A's monthly savings increase by 15%. We know the new income. Now, let's calculate the new savings.

• New Savings: 32 + 15% of 32 = 32 + 4.8 = 36.8 units

So, A's savings increase from 32 units to 36.8 units. This is a great move for A's financial health! Notice that although the savings increased, we don't know how much money A spent. We need to find this. This is because we know the income and savings, but we don't know the expenditure. Time to calculate.

Calculating the New Expenditure

Now, we know the new income (125 units) and the new savings (36.8 units). To find the new expenditure, we simply subtract the new savings from the new income:

• New Expenditure: New Income - New Savings = 125 - 36.8 = 88.2 units

So, A's new expenditure is 88.2 units. This is how much A is spending after the changes. Let's see how to find the percentage increase in expenditure. This is what the problem is asking.

Finding the Percentage Increase in Expenditure

Now, the problem asks for the percentage increase in A's monthly expenditure. Here's how we calculate it:

1. Calculate the increase in expenditure: New Expenditure - Initial Expenditure = 88.2 - 68 = 20.2 units
2. Calculate the percentage increase: (Increase in Expenditure / Initial Expenditure) * 100 = (20.2 / 68) * 100 ≈ 29.7%

So, the percentage increase in A's monthly expenditure is approximately 29.7%. This means that A's spending has increased by about 29.7% due to the increase in income and savings. This is how it's done! Now you know how to find the expenditure percentage.

Key Takeaways and Final Thoughts

• Changes in income directly affect spending and savings.
• Percentage calculations are essential for understanding these changes.
• By breaking down the problem step by step, it becomes much easier to solve.

Summary

This problem highlights how changes in income impact spending and savings. By calculating the new income, new savings, and new expenditure, we were able to determine the percentage increase in expenditure. Understanding these financial dynamics is crucial for personal finance management. So, the next time you see a percentage problem, remember the steps we took and you'll be able to solve it with ease! Well done, guys! You've successfully solved a financial puzzle and have a better understanding of how income and expenditure work together! Now you're ready to handle similar problems with confidence. Keep practicing, and you'll become a financial whiz in no time!