A Mathematical Puzzle Solved: How Much Money Did He Originally Have?

Mathematics is a field that often presents us with intriguing puzzles and riddles. One such riddle involves a boy who has enough money to buy a certain number of exercise books. In this article, we will delve into a particular mathematical problem and see how we can solve it step-by-step using logical reasoning and basic algebra. The riddle is as follows:

The Riddle

"A boy has enough money to buy 20 exercise books. If each book cost 25 paise less, he could buy two more books and still have 70 paise left. How much money had he originally?"

Step-by-Step Solution

To solve this problem, we will break it down into smaller, manageable steps. Let's start by defining the variables and setting up the equations.

Step 1: Define the Variables

Let x be the original cost of one exercise book (in paise). Let y be the total amount of money the boy had originally (in paise).

Step 2: Set Up the Equations

From the problem, we can write two key equations:

The boy can buy 20 books with his original money: If each book costs 25 paise less, he can buy 22 books and have 70 paise left.

These conditions can be written mathematically as:

2 y

22(x - 25) 70 y

Step 3: Solve the Equations

We now have a system of two equations:

2 y 22(x - 25) 70 y

Let's solve this system step-by-step:

Step 3.1: Substitute the Value of y from the First Equation

Since (2 y), we can substitute (2) for (y) in the second equation:

22(x - 25) 70 2

Step 3.2: Simplify the Equation

22(x - 25) 70 2

22x - 550 70 2

22x - 480 2

22x - 2 480

2x 480

x 240 paise

Now that we know the original cost of one book, we can find the total amount of money he had originally:

y 2

y 20 × 240 4800 paise

Converting 4800 paise to Indian Rupees (Rs),

y 4800/100 Rs 48

Conclusion

The boy originally had Rs 48.

Additional Insights

This mathematical puzzle is not only fun but also a great example of how practical problem-solving skills can be applied to real-life situations. Solving such riddles can enhance one's logical thinking and mathematical skills.

Key Learning Points

Understanding how to translate word problems into mathematical equations. Using algebraic methods to solve equations. Logical reasoning and step-by-step problem solving.

Further Exploration

For those interested in further exploring this topic, consider the following:

Explore similar riddles involving different numbers and conditions. Use this method to solve more complex real-world problems. Practice solving riddles that involve fractions and percentages to enhance your skills.

Mathematics is indeed a fascinating field that combines logic, creativity, and problem-solving skills. By engaging with puzzles and riddles like this one, you can improve your mathematical abilities and enjoy the process of solving challenging problems.