The difference between a number and its three fifth is 50. What is the value of the number?

Introduction / Context:
This question tests your ability to translate a verbal statement involving fractions into an algebraic equation. The phrase three fifth of a number appears frequently in quantitative problems, and you must correctly interpret the difference between the number and its fractional part. Solving the resulting linear equation gives the value of the original number.

Given Data / Assumptions:

• Let the unknown be a number x.
• The expression three fifth of the number means (3 / 5) * x.
• The difference between the number x and its three fifth is equal to 50.
• We must determine the exact value of x.

Concept / Approach:
The key concept is forming an equation from the verbal description. The difference between the number and its three fifth is written as x − (3 / 5) * x. This expression can be simplified using fraction operations and then set equal to 50. The resulting algebraic equation is straightforward to solve. Once we find x, we can check the answer by substituting back into the original relationship.

Step-by-Step Solution:
Step 1: Let the unknown number be x. Step 2: The three fifth of x is (3 / 5) * x. Step 3: The problem states that the difference between x and its three fifth is 50, so write x − (3 / 5) * x = 50. Step 4: Factor x on the left side: x * (1 − 3 / 5) = 50. Step 5: Simplify the bracket: 1 − 3 / 5 = 2 / 5. Step 6: The equation becomes x * (2 / 5) = 50. Step 7: Solve for x by multiplying both sides by 5 / 2: x = 50 * (5 / 2). Step 8: Compute the product: 50 * (5 / 2) = 25 * 5 = 125. Step 9: Therefore, the number x is 125.

Verification / Alternative check:
Check the answer by substituting x = 125 back into the original condition. Three fifth of 125 is (3 / 5) * 125 = 3 * 25 = 75. The difference between 125 and 75 is 125 − 75 = 50, which matches the given statement. None of the other options will produce a difference of exactly 50 when you subtract three fifth of the number from the number itself. This confirms that 125 is the correct solution.

Why Other Options Are Wrong:
If the number were 75, three fifth of 75 would be 45 and the difference would be 30, not 50. For 100, three fifth is 60 and the difference is 40. For 150, three fifth is 90 and the difference is 60. For 200, three fifth is 120 and the difference is 80. None of these match the required difference of 50. Only 125 gives three fifth equal to 75 and a difference of exactly 50.

Common Pitfalls:
A common pitfall is misinterpreting the phrase three fifth of the number and writing (x / 3) * 5 or some other incorrect expression. Another frequent error is to reverse the subtraction and compute (3 / 5) * x − x instead of x − (3 / 5) * x, which changes the equation completely. Careful reading and writing the algebra in small steps helps avoid these mistakes. Always verify by plugging the final answer back into the original wording of the question.

Final Answer:
The value of the number is 125.