Linear equation with fractions — If one-fifth of a number decreased by 5 equals 5, find the original number. Model the statement precisely and solve.

Introduction / Context:Verbal equations involving fractions occur frequently in aptitude tests. Converting “one-fifth of a number decreased by 5 is 5” into algebra allows you to compute the unknown quickly and reliably.

Given Data / Assumptions:

• Let the number be n.
• One-fifth of n is n/5.
• “Decreased by 5” means subtract 5.
• Equation: n/5 - 5 = 5.

Concept / Approach:Use the standard method for linear equations with fractions: isolate the fraction term, then clear denominators by multiplying both sides appropriately. Keep arithmetic tidy to avoid errors.

Step-by-Step Solution:Start with n/5 - 5 = 5.Add 5 to both sides: n/5 = 10.Multiply both sides by 5: n = 10 * 5 = 50.

Verification / Alternative check:Check n = 50: one-fifth is 10; 10 - 5 = 5, which matches the condition exactly. Therefore, the solution is correct.

Why Other Options Are Wrong:

• 25/60/75/40: Substituting any of these does not satisfy n/5 - 5 = 5; you will get a value different from 5.

Common Pitfalls:Misreading “decreased by 5” as division; forgetting to add 5 to both sides; arithmetic slips when clearing denominators. Always verify by substitution.

Final Answer:50