If 3/5th part of 60% of a number is 36, then that number is

Concept: When a fraction of a percentage of an unknown number x gives a stated result, write the fraction and the percentage as two multipliers of x, combine them into one multiplier, and divide the given result by that combined multiplier to recover x.

Application:

1. Let the required number be x.

2. 60% of x = 60/100 × x = 3x/5.

3. 3/5th of that quantity = 3/5 × 3x/5 = 9x/25.

4. This equals the given value: 9x/25 = 36.

5. Solve for x: x = 36 × 25/9 = 100.

Cross-check: 60% of 100 = 60, and 3/5 of 60 = 36, which matches the value stated in the question.

Result: The required number is 100.