If 40% of 60% of 3/5 of a number is 504, what will be the 25% of 2/5 of that number?

Options

A. 350
B. 150
C. 175
D. 230

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Set up the equation based on the problem statement
We know that:
\[ 40\% \text{ of } 60\% \text{ of } \frac{3}{5} \text{ of } x = 504 \]

### Step 2: Convert percentages to fractions
Convert the percentages to fractions:
\[ 40\% = \frac{40}{100} = \frac{2}{5} \]
\[ 60\% = \frac{60}{100} = \frac{3}{5} \]

### Step 3: Substitute the fractions into the equation
Now substitute these fractions into the equation:
\[ \frac{2}{5} \times \frac{3}{5} \times \frac{3}{5} \times x = 504 \]

### Step 4: Simplify the left side
Multiply the fractions:
\[ \frac{2 \times 3 \times 3}{5 \times 5 \times 5} \times x = 504 \]
This simplifies to:
\[ \frac{18}{125} x = 504 \]

### Step 5: Solve for \( x \)
To isolate \( x \), multiply both sides by the reciprocal of \( \frac{18}{125} \):
\[ x = 504 \times \frac{125}{18} \]

### Step 6: Calculate \( x \)
Now perform the multiplication:
\[ x = 504 \times \frac{125}{18} \]
Calculating \( 504 \div 18 = 28 \):
\[ x = 28 \times 125 \]
\[ x = 3500 \]

### Step 7: Find \( 25\% \) of \( \frac{2}{5} \) of \( x \)
Now we need to find \( 25\% \) of \( \frac{2}{5} \) of \( x \):
\[ 25\% = \frac{25}{100} = \frac{1}{4} \]
So,
\[ \frac{1}{4} \times \frac{2}{5} \times x = \frac{1}{4} \times \frac{2}{5} \times 3500 \]

### Step 8: Simplify the expression
Calculating \( \frac{2}{5} \times 3500 \):
\[ \frac{2 \times 3500}{5} = \frac{7000}{5} = 1400 \]
Now calculate \( \frac{1}{4} \times 1400 \):
\[ \frac{1400}{4} = 350 \]

### Final Answer
Thus, \( 25\% \) of \( \frac{2}{5} \) of that number is \( 350 \).

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