What will come in place of question mark (?) in the following questions
`((4)/(7) xx (14)/(5) div 2) - ((3)/(10) "of ?") = (4)/(5) - 3`

Options

A. 10
B. 8
C. 9
D. 11

Answer

To solve the equation given in the question, we will follow the steps systematically. The equation is:

\[ \left(\frac{4}{7} \times \frac{14}{5} \div 2\right) - \left(\frac{3}{10} \text{ of } ?\right) = \frac{4}{5} - 3 \]

### Step 1: Simplify the Left Side of the Equation
First, we need to simplify the left side of the equation. We start with the expression:

\[ \frac{4}{7} \times \frac{14}{5} \div 2 \]

We can rewrite the division by 2 as multiplication by \(\frac{1}{2}\):

\[ \frac{4}{7} \times \frac{14}{5} \times \frac{1}{2} \]

### Step 2: Calculate the Multiplication
Now, we can multiply the fractions:

\[ \frac{4 \times 14}{7 \times 5 \times 2} \]

Calculating the numerator and denominator:

\[ = \frac{56}{70} \]

### Step 3: Simplify the Fraction
Now, we simplify \(\frac{56}{70}\):

\[ = \frac{56 \div 14}{70 \div 14} = \frac{4}{5} \]

### Step 4: Substitute Back into the Equation
Now we substitute this back into the original equation:

\[ \frac{4}{5} - \left(\frac{3}{10} \text{ of } ?\right) = \frac{4}{5} - 3 \]

### Step 5: Simplify the Right Side
Now, simplify the right side:

\[ \frac{4}{5} - 3 = \frac{4}{5} - \frac{15}{5} = \frac{4 - 15}{5} = \frac{-11}{5} \]

### Step 6: Set Up the Equation
Now we have:

\[ \frac{4}{5} - \left(\frac{3}{10} \times ?\right) = \frac{-11}{5} \]

### Step 7: Isolate the Term with ?
To isolate the term with the question mark, we can rearrange the equation:

\[ -\left(\frac{3}{10} \times ?\right) = \frac{-11}{5} - \frac{4}{5} \]

Combining the fractions on the right side:

\[ -\left(\frac{3}{10} \times ?\right) = \frac{-15}{5} = -3 \]

### Step 8: Remove the Negative Sign
Multiplying both sides by -1 gives:

\[ \frac{3}{10} \times ? = 3 \]

### Step 9: Solve for ?
Now, to find \( ? \), we can multiply both sides by \(\frac{10}{3}\):

\[ ? = 3 \times \frac{10}{3} = 10 \]

Thus, the value that comes in place of the question mark is:

\[ \boxed{10} \]