Two-fifth of thirty percent of one-fourth of a number is 15. What is 20 percent of that number ?

Options

A. 90
B. 150
C. 100
D. 120

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We need to find a number \( x \) such that two-fifths of thirty percent of one-fourth of \( x \) equals 15.

### Step 2: Set Up the Equation
We can express the problem mathematically:
\[ \frac{2}{5} \times 30\% \times \frac{1}{4} \times x = 15 \]
First, convert 30% to a fraction:
\[ 30\% = \frac{30}{100} = \frac{3}{10} \]
Now substitute this into the equation:
\[ \frac{2}{5} \times \frac{3}{10} \times \frac{1}{4} \times x = 15 \]

### Step 3: Simplify the Left Side
Now, simplify the left side:
\[ \frac{2 \times 3 \times 1}{5 \times 10 \times 4} \times x = 15 \]
Calculating the numerator and denominator:
\[ \frac{6}{200} \times x = 15 \]
This simplifies to:
\[ \frac{3}{100} \times x = 15 \]

### Step 4: Solve for \( x \)
To isolate \( x \), multiply both sides by the reciprocal of \( \frac{3}{100} \):
\[ x = 15 \times \frac{100}{3} \]
Calculating this gives:
\[ x = \frac{1500}{3} = 500 \]

### Step 5: Find 20% of \( x \)
Now that we have \( x = 500 \), we need to find 20% of \( x \):
\[ 20\% \text{ of } x = \frac{20}{100} \times 500 \]
This simplifies to:
\[ \frac{1}{5} \times 500 = 100 \]

### Final Answer
Thus, 20% of the number is:
\[ \boxed{100} \]

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