When 35 is subtracted from a number, the result is 80 percent of the original number. What is four-fifths of that original number?

Introduction / Context:
This problem tests the relationship between a number and a percentage of itself when a fixed value is subtracted. We are told that subtracting 35 from an unknown number gives 80 percent of that number. Once the original number is found using algebra, we are asked to compute four-fifths of it. This style of question is very common in aptitude exams.

Given Data / Assumptions:

• Let the original number be N.
• When 35 is subtracted from N, the result equals 80 percent of N.
• We must find four-fifths (4/5) of the original number N.
• All values are real numbers, and we expect an integer answer from the options.

Concept / Approach:
The key concept is that 80 percent of a number is 0.8 times that number. The condition can be expressed as an equation involving N. From that equation, we solve for N. Once N is known, calculating four-fifths of N is straightforward. It is often easier to work with decimal 0.8 or the fraction 4/5 as required, keeping arithmetic simple.

Step-by-Step Solution:
Step 1: Let the original number be N.Step 2: The condition is that N minus 35 equals 80 percent of N. In equation form, N - 35 = 0.8N.Step 3: Rearrange the equation by bringing 0.8N to the left: N - 0.8N - 35 = 0, which gives 0.2N - 35 = 0.Step 4: Solve for N: 0.2N = 35, so N = 35 / 0.2.Step 5: Since 0.2 equals 1/5, dividing by 0.2 is the same as multiplying by 5. Therefore N = 35 * 5 = 175.Step 6: Find four-fifths of N: (4/5) * 175 = 4 * 35 = 140.

Verification / Alternative check:
We can verify by substituting N = 175 back into the original condition. Subtracting 35 gives 175 - 35 = 140. Now compute 80 percent of 175: 0.8 * 175 = 140. Since both sides give 140, the equation holds. Next, four-fifths of 175 is indeed (4 * 175) / 5 = 700 / 5 = 140. Everything is consistent, confirming that 140 is correct.

Why Other Options Are Wrong:
The value 175 is the original number, not four-fifths of it. The value 135 is less than 140 and does not satisfy the condition when used as four-fifths of the original. The value 95 is much too small and would not match the percentage relationship. The value 210 exceeds the original number 175, which is impossible for four-fifths of N. Only 140 correctly represents four-fifths of the computed original number.

Common Pitfalls:
Some students mistakenly set up the equation as N - 35 = 0.8 * 35 instead of 0.8N. Others misinterpret 80 percent as 8 or 0.08, which leads to incorrect calculations. Forgetting that 0.2 equals 1/5 can also complicate the arithmetic. Working carefully with the decimal representations and rearranging the equation step by step helps avoid these errors.

Final Answer:
Four-fifths of the original number is 140, so the correct option is 140.