To solve the problem, let's carefully break down the given information and work step by step to find the number.
1. Let the number be [tex]\( x \)[/tex].
2. We are given that 60% of [tex]\(\frac{3}{5}\)[/tex] of [tex]\( x \)[/tex] is equal to 36. This can be written down as an equation:
[tex]\[
0.60 \times \left(\frac{3}{5} \times x\right) = 36
\][/tex]
3. First, simplify the expression inside the parentheses:
[tex]\[
\frac{3}{5} \times x = \frac{3x}{5}
\][/tex]
4. Now substitute [tex]\(\frac{3x}{5}\)[/tex] back into the equation:
[tex]\[
0.60 \times \frac{3x}{5} = 36
\][/tex]
5. Convert 0.60 to a fraction for easier multiplication:
[tex]\[
0.60 = \frac{60}{100} = \frac{3}{5}
\][/tex]
6. Now, substitute [tex]\(\frac{3}{5}\)[/tex] for 0.60 in the equation:
[tex]\[
\left(\frac{3}{5}\right) \times \left(\frac{3x}{5}\right) = 36
\][/tex]
7. Multiply the fractions on the left-hand side:
[tex]\[
\frac{3}{5} \times \frac{3x}{5} = \frac{9x}{25}
\][/tex]
8. This gives us a new equation:
[tex]\[
\frac{9x}{25} = 36
\][/tex]
9. To solve for [tex]\( x \)[/tex], multiply both sides of the equation by 25 to get rid of the denominator:
[tex]\[
9x = 36 \times 25
\][/tex]
10. Calculate [tex]\( 36 \times 25 \)[/tex]:
[tex]\[
36 \times 25 = 900
\][/tex]
11. Now, solve for [tex]\( x \)[/tex] by dividing both sides by 9:
[tex]\[
x = \frac{900}{9}
\][/tex]
12. Calculate [tex]\(\frac{900}{9}\)[/tex]:
[tex]\[
x = 100
\][/tex]
Therefore, the number is [tex]\( 100 \)[/tex]. The correct answer is:
[tex]\[
\boxed{100}
\][/tex]
