Finding the Original Number After a Percentage Decrease

The problem asks us to find an original number. We are told that when this number is decreased by 6%, the result is 3760.

Understanding Percentage Decrease

When a number is decreased by a certain percentage, it means we are subtracting that percentage of the original number from the number itself. A 6% decrease means we are left with $100\% - 6\% = 94\%$ of the original number.

Setting Up the Equation

Let the original number be represented by the variable '$x$'.

According to the problem statement:

• The number is decreased by 6%.
• The result is 3760.

This can be written mathematically as:

Original Number - (6% of Original Number) = 3760

In terms of '$x$':

$ x - (0.06 \times x) = 3760 $

Alternatively, we can directly use the remaining percentage:

$ (100\% - 6\%) \text{ of } x = 3760 $

$ 94\% \text{ of } x = 3760 $

Converting the percentage to a decimal:

$ 0.94 \times x = 3760 $

Calculating the Number

To find the value of '$x$', we need to isolate it by dividing both sides of the equation by 0.94:

$ x = \frac{3760}{0.94} $

Now, let's perform the division:

$ x = 4000 $

Verification

We can check our answer by decreasing 4000 by 6%:

6% of 4000 is $0.06 \times 4000 = 240$.

Decreasing 4000 by 240 gives:

$ 4000 - 240 = 3760 $

This matches the result given in the question, confirming our calculation.

Conclusion

The original number is 4000.