Income & Savings Problems: Detailed Solutions

Hey guys! Let's dive into some interesting math problems. We're going to break down how to solve income and expenditure questions step-by-step. These are pretty common in various exams, so understanding them is super important. We'll be using the questions you provided as examples. Get ready to flex those math muscles!

Question 16: Monthly Income and Savings Calculation

Alright, let's tackle the first problem. The crux of the first question involves calculating how a change in income impacts spending when savings remain constant. This type of problem is a classic and tests your ability to work with percentages and basic arithmetic. Let's break it down into easy-to-understand steps.

Here’s the original question, just to keep us on the same page:

*A person's monthly income is Rs 15,000. He saves 20% of his income. If his income increases by 10%, but there is no change in his savings, then how much does he spend now?

A- 13,500 B. 13,000 C. 14000 D. 14,500*

Okay, first things first, let's find out how much the person saves initially. We know his income is Rs 15,000, and he saves 20% of it. To calculate the savings, we do the following:

• Savings = (20 / 100) * 15,000 = Rs 3,000.*

So, the person saves Rs 3,000 per month. This means he spends the rest of his income. The initial expenditure is calculated as:

• Expenditure = Income - Savings = 15,000 - 3,000 = Rs 12,000.*

Now comes the fun part! His income increases by 10%. Let's calculate the new income:

• New Income = 15,000 + (10 / 100) * 15,000 = 15,000 + 1,500 = Rs 16,500.*

The question says his savings remain unchanged. So, he still saves Rs 3,000. To find out his new expenditure, we use this formula:

• New Expenditure = New Income - Savings = 16,500 - 3,000 = Rs 13,500.*

Therefore, the correct answer is A. Rs 13,500. See? It wasn't so tough, right?

Key Takeaways

• Always start by understanding the initial conditions.
• Calculate savings and expenditure separately.
• Apply the percentage increase to find the new income.
• Use the new income and unchanged savings to calculate the new expenditure.

Remember, the core concept here is understanding how income, savings, and expenditure are interrelated. Practicing similar problems will help you master this concept. Don’t be afraid to take it slow and break down the problem into smaller steps. You’ve got this!

Question 17: Train Speed and Distance (Incomplete Question)

I noticed the second question is incomplete, so, unfortunately, I can't provide a solution for that. To help you with similar problems, here's what you need to solve train-related problems effectively. We'll use a hypothetical scenario to demonstrate the process.

Let's assume the question was something like this: “A train is moving at a speed of 60 km/h. If it has to cover a distance of 300 km, how much time will it take?”

To solve this, we'll use the formula:

• Time = Distance / Speed*

Here's how we'd do it step by step:

1. Identify the Given Values: We know that the speed of the train is 60 km/h, and the distance it needs to cover is 300 km.
2. Apply the Formula: Plug the values into the formula: Time = 300 km / 60 km/h = 5 hours
3. The Answer: The train will take 5 hours to cover the distance.

Common Variations

• Converting Units: Sometimes, you might need to convert units. For example, if the speed is given in meters per second (m/s) and the distance in kilometers, you'll need to convert them to consistent units.
• Relative Speed: If two trains are involved, you'll need to consider their relative speed. If they are moving in the same direction, subtract their speeds. If they're moving in opposite directions, add their speeds.
• Length of the Train and Objects: Problems might involve the length of the train and the length of bridges or platforms. In such cases, the total distance to be covered is the sum of these lengths.

Tips for Success

• Draw Diagrams: Visual aids can be super helpful, especially for problems involving trains crossing bridges or other trains.
• Understand the Concepts: Make sure you understand the relationship between speed, distance, and time.
• Practice Regularly: The more problems you solve, the better you'll become at recognizing the patterns and applying the formulas.

In order to provide you with a solution, the question will require you to define clearly the parameters needed to solve the problem, if not, it will be impossible.

Tips for Tackling Income and Expenditure Problems Effectively

Alright, let’s get you prepped to ace these types of questions. Here are some extra tips and tricks to make sure you're well-equipped to tackle any income and expenditure problem that comes your way.

1. Read Carefully: The most important thing, seriously, is to read the question carefully. Underline or highlight the key information. Make sure you fully understand what the question is asking before you start solving it.
2. Identify the Variables: Clearly identify the variables involved – income, savings, expenditure, and any changes in these. Write them down separately to avoid confusion.
3. Use Formulas: Know and use the correct formulas. For example:
   • Savings = Income - Expenditure
   • Expenditure = Income - Savings
   • Percentage = (Part / Whole) * 100
4. Work with Percentages: Be comfortable with percentages. Know how to calculate percentages of a number and how to increase or decrease a number by a certain percentage.
5. Break Down Complex Problems: If the problem seems complex, break it down into smaller, manageable steps. This will make it easier to solve and reduce the chances of errors.
6. Practice, Practice, Practice: The more you practice, the more confident you will become. Solve a variety of problems to understand the different types and how to approach them.
7. Check Your Answers: Always double-check your answers. Make sure your answer makes sense in the context of the problem.
8. Time Management: In exams, time is of the essence. Practice solving problems within a time limit to improve your speed and accuracy.
9. Don't Panic: If you get stuck on a problem, don't panic. Take a deep breath, reread the question, and try a different approach.
10. Seek Help: Don't hesitate to ask for help from your teacher, classmates, or online resources if you're struggling with a concept.

By following these tips and practicing regularly, you’ll be well on your way to mastering these problems. Keep up the great work, and don't be afraid to ask questions. Good luck, and keep those math skills sharp!