Calculating the Original Sum

Oct 13, 2025 by talynt.org 37 views

Understanding the Problem

In this problem, we are given that Hassan has Rs. 1400 left after spending 30% of his money. We need to find the original sum of money that Hassan had. This is a classic problem of percentage calculation, and we will use the concept of percentage to solve it.

Calculating the Original Sum

Let's assume that Hassan's original sum of money is x. Since he spent 30% of his money, the amount left is 70% of his original sum. We can write this as:

70% of x = 1400

To find the original sum, we need to convert the percentage to a decimal and then divide 1400 by the decimal value.

Converting Percentage to Decimal

To convert a percentage to a decimal, we divide the percentage value by 100.

70% = 70/100 = 0.7

Solving for x

Now that we have the decimal value, we can set up the equation:

0.7x = 1400

To solve for x, we need to divide both sides of the equation by 0.7.

x = 1400/0.7

x = 2000

Conclusion

Therefore, Hassan had Rs. 2000 originally.

Example Solution

Let's take a look at an example solution to this problem.

Suppose Hassan had Rs. 2000 originally and spent 30% of it. The amount spent would be:

30% of 2000 = 0.3 x 2000 = 600

The amount left would be:

2000 - 600 = 1400

This confirms our solution that Hassan had Rs. 2000 originally.

Real-World Application

This problem has a real-world application in finance and accounting. When calculating taxes, interest rates, or investment returns, we often need to calculate percentages of a given amount. This problem helps us understand how to calculate percentages and apply them to real-world scenarios.

Tips and Tricks

Here are some tips and tricks to help you solve percentage problems like this one:

Always convert percentages to decimals before performing calculations.
Use the formula: (percentage/100) x (original amount) to calculate the amount.
Check your units and make sure they are consistent.
Use examples to verify your solution.

Practice Problems

Here are some practice problems to help you practice calculating percentages:

A shirt is on sale for 20% off. If the original price is Rs. 1000, how much will you pay?
A bank offers a 5% interest rate on deposits. If you deposit Rs. 5000, how much will you earn in interest?
A company offers a 10% discount on all purchases. If you buy a product for Rs. 2000, how much will you pay?

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to Hassan's original sum of money problem.

Q: What is the original sum of money that Hassan had?

A: The original sum of money that Hassan had is Rs. 2000.

Q: How did you calculate the original sum of money?

A: We calculated the original sum of money by using the concept of percentage. We assumed that Hassan's original sum of money is x. Since he spent 30% of his money, the amount left is 70% of his original sum. We can write this as:

70% of x = 1400

To find the original sum, we need to convert the percentage to a decimal and then divide 1400 by the decimal value.

Q: What is the formula to calculate the original sum of money?

A: The formula to calculate the original sum of money is:

x = (amount left) / (percentage/100)

In this case, the formula becomes:

x = 1400 / (70/100)

x = 1400 / 0.7

x = 2000

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, we divide the percentage value by 100.

For example, to convert 70% to a decimal, we divide 70 by 100:

70% = 70/100 = 0.7

Q: What is the real-world application of this problem?

A: This problem has a real-world application in finance and accounting. When calculating taxes, interest rates, or investment returns, we often need to calculate percentages of a given amount. This problem helps us understand how to calculate percentages and apply them to real-world scenarios.

Q: How do I solve percentage problems like this one?

A: To solve percentage problems like this one, follow these steps:

Convert the percentage to a decimal.
Use the formula: (percentage/100) x (original amount) to calculate the amount.
Check your units and make sure they are consistent.
Use examples to verify your solution.

Q: What are some tips and tricks to help me solve percentage problems?

A: Here are some tips and tricks to help you solve percentage problems:

Always convert percentages to decimals before performing calculations.
Use the formula: (percentage/100) x (original amount) to calculate the amount.
Check your units and make sure they are consistent.
Use examples to verify your solution.

Q: What are some practice problems to help me practice calculating percentages?

A: Here are some practice problems to help you practice calculating percentages:

A shirt is on sale for 20% off. If the original price is Rs. 1000, how much will you pay?
A bank offers a 5% interest rate on deposits. If you deposit Rs. 5000, how much will you earn in interest?
A company offers a 10% discount on all purchases. If you buy a product for Rs. 2000, how much will you pay?

Conclusion

In conclusion, calculating percentages is an essential skill in finance, accounting, and real-world applications. By understanding how to calculate percentages, we can make informed decisions and solve problems with confidence.