When a number is increased by 69, it becomes 103 percent of itself. What is the original number?

Introduction / Context:
This question is a simple application of percentage increase expressed in terms of an absolute increase. It tests algebraic manipulation involving converting a percentage expression into an equation with an unknown number.

Given Data / Assumptions:

• When the number is increased by 69, it becomes 103 percent of the original.
• We need to find the original number.

Concept / Approach:
If the original number is N, then 103 percent of N is 1.03 * N. The statement says that N + 69 equals 1.03 * N. Setting up this equation and solving for N gives the original number.

Step-by-Step Solution:
Let the original number = N.Increased by 69 gives N + 69.Given that N + 69 = 103 percent of N = 1.03 * N.So N + 69 = 1.03N.Rearrange: 1.03N - N = 69.Thus 0.03N = 69.So N = 69 / 0.03 = 69 * (100 / 3) = 2300.

Verification / Alternative check:
Check with N = 2300. Then 103 percent of 2300 is 1.03 * 2300 = 2369. Increasing the original number by 69 yields 2300 + 69 = 2369, exactly matching the stated condition, confirming the result.

Why Other Options Are Wrong:
Numbers like 1300, 3300 or 4300 do not satisfy the relationship N + 69 = 1.03N. Substituting them leads to inconsistencies where the required increase is not 69 or the percentage is not 103 percent.

Common Pitfalls:
Some learners confuse 103 percent with 1.3 or mistakenly divide by 103 instead of 3 in the calculation. Remember that 103 percent means 103/100, so the factor is 1.03, and the extra part beyond the original 100 percent is 3 percent.

Final Answer:
The original number is 2300.