If 60% of three fifths of a number is equal to 36, what is the original number?

Introduction / Context:
This question combines percentages and fractions. We are told that 60 percent of three fifths of an unknown number is 36, and we are asked to find the original number. Such problems are common in percentage and ratio sections of aptitude tests and require careful translation of verbal statements into algebraic expressions.

Given Data / Assumptions:
Let the original number be N.Three fifths of the number is (3 / 5) * N.Sixty percent of that quantity equals 36.We must determine the value of N.

Concept / Approach:
Percentages can be converted into fractions or decimals. Here, 60 percent means 60 / 100 = 3 / 5. The phrase 60 percent of three fifths of N becomes (3 / 5) of (3 / 5 * N). Setting this equal to 36 gives a simple equation in N. Solving this equation will provide the required value of the original number.

Step-by-Step Solution:
Step 1: Express 60 percent as a fraction: 60% = 3 / 5.Step 2: Three fifths of N is (3 / 5) * N.Step 3: Sixty percent of three fifths of N is (3 / 5) * (3 / 5 * N) = (9 / 25) * N.Step 4: According to the problem, (9 / 25) * N = 36.Step 5: Multiply both sides of the equation by 25 to remove the denominator: 9N = 36 * 25.Step 6: Compute 36 * 25. First, 25 * 30 = 750 and 25 * 6 = 150, so the total is 900.Step 7: Now we have 9N = 900.Step 8: Divide both sides by 9: N = 900 / 9 = 100.

Verification / Alternative check:
Check the result by substituting N = 100 back into the description. Three fifths of 100 is (3 / 5) * 100 = 60. Sixty percent of 60 is 60 / 100 * 60 = 36. This matches the given value in the problem statement, confirming that N = 100 is correct.

Why Other Options Are Wrong:
If N were 86, then three fifths would be 51.6 and 60 percent of that would be approximately 30.96, not 36. For N = 94, three fifths is 56.4 and 60 percent of that is 33.84. For N = 115, three fifths is 69 and 60 percent of that is 41.4. None of these match the required value of 36, so these options are incorrect.

Common Pitfalls:
Some learners misinterpret the phrase 60 percent of three fifths of a number and either apply 60 percent directly to the original number or add fractions instead of multiplying them. Others convert percentages and fractions inconsistently, leading to errors in the equation. Writing each step carefully in fraction form helps prevent mistakes.

Final Answer:
The original number is 100.