In a percentage problem, 60% of 3/5 of a certain number is equal to 36. What is the value of that original number?

Introduction:
This question checks your understanding of percentages and fractions applied together to an unknown number. You are told that 60% of three fifths of a number equals 36, and you must find the original number. Such problems are very common in quantitative aptitude exams.

Given Data / Assumptions:

• Let the original number be N.
• Three fifths of the number is (3/5) * N.
• Sixty percent (60%) of this quantity is equal to 36.
• We assume N is a real positive number.

Concept / Approach:
Percentages can be written as fractions or decimals. Here, 60% = 60/100 = 3/5. The statement “60% of 3/5 of N is 36” becomes a simple linear equation in N. We multiply the fractions, set equal to 36, and then solve for N using basic algebra.

Step-by-Step Solution:
Step 1: Write the mathematical expression.60% of (3/5 of N) = 36Step 2: Convert 60% to fraction.(60/100) * (3/5 * N) = 36Step 3: Simplify the fractions.(3/5) * (3/5) * N = 36(9/25) * N = 36Step 4: Solve for N.N = 36 * (25/9)N = (36/9) * 25 = 4 * 25 = 100

Verification / Alternative check:
Check by working forward from N = 100. Three fifths of 100 is (3/5) * 100 = 60. Then 60% of 60 is (60/100) * 60 = 36. This confirms that N = 100 satisfies the condition perfectly.

Why Other Options Are Wrong:
94, 115, 86 and 120 do not satisfy the relationship when you compute 3/5 of the number and then take 60% of that result. Only 100 produces 36 at the end of the two-step percentage calculation.

Common Pitfalls:
A common mistake is to treat the statement as “60% of the number is 36” or as “3/5 of 36 is 60%”, which reverses the operations. Another mistake is to add percentages instead of multiplying them when they are applied successively to the same number.

Final Answer:
The original number is 100.