Solving a Coinage Puzzle: A Mathematical Approach to Currency Values

Recently, a intriguing coinage puzzle has been circulating, challenging our ability to solve equations and understand currency values. The problem itself involves a person named Sita who has a certain amount of money in 50 paise and 25 paise coins, and the question is about the exact count of these coins. Let's delve into the solution of this intriguing puzzle step by step.

Understanding the Puzzle

The puzzle states that Sita has 9 rupees in 50 paise and 25 paise coins. Furthermore, she has twice as many 25 paise coins as 50 paise coins. This means if we denote the number of 50 paise coins as x, then the number of 25 paise coins would be 2x. Our task is to determine how many 50 paise and 25 paise coins she has.

Step-by-Step Solution

First, let's convert the 9 rupees into paise since it simplifies calculations. 9 rupees is equivalent to 900 paise. Now, we can set up an equation based on the total value formula:

Total Value (Number of 50 paise coins × Value of 50 paise) (Number of 25 paise coins × Value of 25 paise)

Substituting the known values:

900 (x × 50) (2x × 25)

This simplifies to:

900 5 5

900 10

Solving for x:

x 900 / 100 9

Thus, Sita has 9 50 paise coins.

Since the number of 25 paise coins is twice the number of 50 paise coins, we have:

2x 2 × 9 18

So, Sita has 18 25 paise coins.

The total number of coins is:

Total coins 50 paise coins 25 paise coins 9 18 27

Conclusion

In conclusion, Sita has 27 coins in total, consisting of 9 50 paise coins and 18 25 paise coins.

Alternate Solutions

Several other solutions have been proposed, each with their own unique approach:

One solution directly converts the total value into paise, setting up the equation and solving for x similarly as mentioned above. Another solution reinterprets the total number of coins based on the given value, leading to the same numerical results. A third approach redefines variables but arrives at the same conclusion with a different setup and simplification process.

Regardless of the approach taken, the fundamental mathematical principles and steps remain consistent, leading to the solution of 9 50 paise coins and 18 25 paise coins, summing up to a total of 27 coins.

The puzzle not only tests our understanding of basic arithmetic but also challenges our problem-solving skills, making it a delightful exercise for both amateurs and mathematicians alike.