`(3)/(4)` of `(1)/(7)` of a number 120, then the number

Options

A. 1120
B. 560
C. 280
D. 140

Answer

To solve the problem step by step, we need to find a number \( x \) such that \( \frac{3}{4} \) of \( \frac{1}{7} \) of \( x \) equals 120.

### Step 1: Set up the equation
We start by expressing the problem mathematically. We know that:

\[ \frac{3}{4} \times \frac{1}{7} \times x = 120 \]

### Step 2: Simplify the left side
Now, we can simplify the left side of the equation:

\[ \frac{3}{4} \times \frac{1}{7} = \frac{3 \times 1}{4 \times 7} = \frac{3}{28} \]

So, we can rewrite the equation as:

\[ \frac{3}{28} \times x = 120 \]

### Step 3: Solve for \( x \)
To isolate \( x \), we can multiply both sides of the equation by the reciprocal of \( \frac{3}{28} \), which is \( \frac{28}{3} \):

\[ x = 120 \times \frac{28}{3} \]

### Step 4: Calculate \( x \)
Now we perform the multiplication:

\[ x = 120 \times \frac{28}{3} = \frac{120 \times 28}{3} \]

Calculating \( 120 \times 28 \):

\[ 120 \times 28 = 3360 \]

Now, divide by 3:

\[ x = \frac{3360}{3} = 1120 \]

### Final Answer
Thus, the number \( x \) is:

\[ \boxed{1120} \]