Find the value of question mark (?) in the following questions given below
`(19)/(23) -: (361)/(529)= 2 ""(3)/(19)- ?`

Options

A. `(15)/(19)`
B. `(16)/(19)`
C. `(17)/(19)`
D. `(18)/(19)`

Answer

To find the value of the question mark (?) in the equation

\[ \frac{19}{23} \div \frac{361}{529} = \frac{2}{3} \left( \frac{3}{19} - ? \right) \]

we can follow these steps:

### Step 1: Simplify the left side of the equation
We start with the left side:

\[ \frac{19}{23} \div \frac{361}{529} \]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{19}{23} \times \frac{529}{361} \]

### Step 2: Simplify the fractions
Next, we can simplify the fractions. Notice that \(361 = 19^2\) and \(529 = 23^2\):

\[ \frac{19}{23} \times \frac{23^2}{19^2} \]

This simplifies to:

\[ \frac{19 \cdot 23^2}{23 \cdot 19^2} = \frac{23}{19} \]

### Step 3: Set up the equation
Now we have:

\[ \frac{23}{19} = \frac{2}{3} \left( \frac{3}{19} - ? \right) \]

### Step 4: Multiply both sides by \(3\)
To eliminate the fraction on the right side, we can multiply both sides by \(3\):

\[ 3 \cdot \frac{23}{19} = 2 \left( \frac{3}{19} - ? \right) \]

This gives us:

\[ \frac{69}{19} = 2 \left( \frac{3}{19} - ? \right) \]

### Step 5: Divide both sides by \(2\)
Now, divide both sides by \(2\):

\[ \frac{69}{38} = \frac{3}{19} - ? \]

### Step 6: Isolate the question mark (?)
Now, we can isolate the question mark:

\[ ? = \frac{3}{19} - \frac{69}{38} \]

### Step 7: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple of \(19\) and \(38\) is \(38\):

\[ ? = \frac{3 \cdot 2}{38} - \frac{69}{38} = \frac{6 - 69}{38} = \frac{-63}{38} \]

### Step 8: Final answer
Thus, the value of the question mark (?) is:

\[ ? = -\frac{63}{38} \]