When a number is increased by 28, the result becomes 107% of the original number. Using percentage and simple algebra, find the original number.

Introduction / Context:
This arithmetic and percentage question is typical in quantitative aptitude tests. You are told that when a certain number is increased by a fixed amount, the new value is 107 percent of the original number. From this information, you must work backwards to determine the original number. This type of question reinforces the connection between percentage increases and algebraic equations.

Given Data / Assumptions:

• Let the original number be N.
• When the number is increased by 28, the result is N + 28.
• This result equals 107 percent of the original number, that is 1.07N.
• We must find the value of N.
• All quantities are real numbers, and N is positive.

Concept / Approach:
A percentage increase can be represented as a multiplier of the original. An increase to 107 percent of the original means the new value is 1.07 times the original. So we set up the equation N + 28 = 1.07N. This yields a simple linear equation in N, which we solve step by step. Using fractional form instead of decimals is another valid approach, but the decimal representation is convenient here.

Step-by-Step Solution:
Step 1: Let the original number be N.Step 2: After increasing N by 28, we obtain N + 28.Step 3: According to the statement, N + 28 = 107 percent of N = 1.07N.Step 4: Write the equation: N + 28 = 1.07N.Step 5: Subtract N from both sides: 28 = 1.07N − N = 0.07N.Step 6: Solve for N: N = 28 / 0.07.Step 7: Since 0.07 = 7/100, N = 28 ÷ (7/100) = 28 × (100/7) = 4 × 100 = 400.

Verification / Alternative check:
Check the result by substituting N = 400 back into the original relationship. Increasing 400 by 28 gives 400 + 28 = 428. Now compute 107 percent of 400: 1.07 × 400 = 428. Since both methods give 428 as the new value, N = 400 is confirmed as correct.

Why Other Options Are Wrong:
If N were 336, adding 28 would give 364, which is not equal to 1.07 × 336. Similarly, 420, 252, and 280 do not satisfy the equation N + 28 = 1.07N when checked directly. Each of these values produces a mismatch between the left and right sides of the equation. Only 400 yields the correct balance between the increase and the percentage representation.

Common Pitfalls:
A common mistake is to treat the 7 percent increase as 0.7 rather than 0.07, which causes errors in the equation. Another error is to set up the equation as 28 = 1.07N instead of N + 28 = 1.07N. To avoid these mistakes, always translate phrases like 107 percent of the original number into 1.07 times the original and carefully account for the fixed increase in the equation.

Final Answer:
The original number before the increase was 400.