A number, when increased by 30%, becomes 390. What is the original number before the increase?

Introduction / Context:
This question is a direct application of percentage increase. We are told that after a 30% increase, a number becomes 390. The goal is to work backwards to find the original number. This type of reverse percentage calculation is very common in topics like profit and loss, population growth, and price changes.

Given Data / Assumptions:

Let the original number be N.

The number is increased by 30%.

After the increase, the new value is 390.

We need to determine the value of N.

Concept / Approach:
When a quantity is increased by 30%, the new value becomes 1.30 times the original value. In symbols, new value = N * (1 + 30 / 100) = 1.30N. Since we know the new value is 390, we set 1.30N = 390 and solve for N by dividing 390 by 1.30. This is a straightforward linear equation in one variable.

Step-by-Step Solution:
Let the original number be N.After a 30% increase, new number = N * (1 + 30 / 100) = 1.30N.We are given that 1.30N = 390.So N = 390 / 1.30.Compute N: 390 / 1.30 = 39000 / 130 = 300.Therefore, the original number is 300.

Verification / Alternative check:
Check by applying the 30% increase to 300. Thirty percent of 300 is (30 / 100) * 300 = 90. Adding this increase to the original number gives 300 + 90 = 390. This matches the given final value, so the original number 300 is confirmed to be correct.

Why Other Options Are Wrong:

180 increased by 30% becomes 234, not 390.

480 decreased by 30% or increased by 30% does not yield 390.

260 increased by 30% becomes 338, not 390.

240 increased by 30% becomes 312, also not equal to 390.

Common Pitfalls:
Some learners mistakenly treat 30% as 0.30 and subtract it from 390 instead of dividing by 1.30. Others try to compute 70% of 390, assuming that is the original number, which is incorrect in this context. The original number is the base on which the 30% was applied, so we must use division by the factor 1.30 rather than simple subtraction. Thinking in terms of multiplication factors like 1.30 for a 30% increase helps avoid confusion.

Final Answer:
The original number, before it was increased by 30%, is 300.