Three-fifth of two-third of one-sixth of a number is 40 what is thirty percent of that number ?

Options

A. 180
B. 240
C. 480
D. 160

Answer

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

### Step 1: Define the variable
Let the unknown number be represented by \( X \).

### Step 2: Set up the equation
According to the problem, three-fifth of two-third of one-sixth of the number is equal to 40. We can express this mathematically as:
\[ \frac{3}{5} \times \frac{2}{3} \times \frac{1}{6} \times X = 40 \]

### Step 3: Simplify the left side of the equation
Now, we can simplify the left side of the equation:
\[ \frac{3 \times 2 \times 1}{5 \times 3 \times 6} \times X = 40 \]
The \( 3 \) in the numerator and denominator cancels out:
\[ \frac{2}{5 \times 6} \times X = 40 \]
This simplifies to:
\[ \frac{2}{30} \times X = 40 \]
Or:
\[ \frac{1}{15} \times X = 40 \]

### Step 4: Solve for \( X \)
To isolate \( X \), multiply both sides of the equation by 15:
\[ X = 40 \times 15 \]
Calculating the right side gives:
\[ X = 600 \]

### Step 5: Calculate 30% of \( X \)
Now, we need to find 30% of the number \( X \):
\[ 30\% \text{ of } X = \frac{30}{100} \times 600 \]
This simplifies to:
\[ 0.3 \times 600 \]
Calculating this gives:
\[ 0.3 \times 600 = 180 \]

### Final Answer
Thus, 30% of the number is \( \boxed{180} \).

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