When a number is increased by 216, it becomes 140% of its original value. What is the original number?

Introduction / Context:
This is another algebraic percentage problem similar to earlier ones, where a number is increased by a fixed amount and described as a certain percent of itself. The goal is to find the original number by converting the verbal description into an equation and solving it. These types of questions commonly appear in aptitude tests.

Given Data / Assumptions:

• Let the original number be N.
• When 216 is added to N, the result becomes 140% of N.
• We need to find the value of N.

Concept / Approach:
If the final value is 140% of the original, then final value = 1.40 * N. At the same time, the final value is given to be N + 216. Setting N + 216 equal to 1.40N gives a linear equation. Solving this equation provides the original number. Careful handling of decimal multipliers is important.

Step-by-Step Solution:
Step 1: Let the original number be N. Step 2: After increasing it by 216, the new value is N + 216. Step 3: According to the problem, N + 216 = 140% of N. Step 4: Write 140% of N as 1.40N. Step 5: So the equation is N + 216 = 1.40N. Step 6: Rearrange to get 216 = 1.40N - N = 0.40N. Step 7: Therefore N = 216 / 0.40. Step 8: Compute N = 540. Step 9: So the original number is 540.

Verification / Alternative check:
Substitute N = 540 back into the condition. N + 216 = 540 + 216 = 756. Now compute 140% of 540: 1.40 * 540 = 756. Both values match exactly, confirming that N = 540 is correct.

Why Other Options Are Wrong:

• 756: This is the final value after the increase, not the original number.
• 450: 140% of 450 is 630, and 450 + 216 = 666, so the condition is not satisfied.
• 675: 140% of 675 is 945, while 675 + 216 = 891.
• 600: 140% of 600 is 840, while 600 + 216 = 816.

Common Pitfalls:
Students may misinterpret 140% as 1.4 plus N instead of 1.4 times N. Others may perform the algebra incorrectly, for example by moving terms incorrectly or dividing by the wrong coefficient. Double checking the derived number by substituting it back into the original statement is a reliable way to catch such mistakes.

Final Answer:
The original number is 540.