If `(a)/(b)=1-(x)/(y)`, then `(b)/(a)=`

Options

A. `(x)/(y-x)`
B. `(y)/(x)-1`
C. `(y)/(x-y)`
D. `(y)/(y-x)`

Answer

To solve the equation \(\frac{a}{b} = 1 - \frac{x}{y}\) and find the value of \(\frac{b}{a}\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ \frac{a}{b} = 1 - \frac{x}{y} \]

### Step 2: Simplify the right-hand side
To simplify the right-hand side, we can express \(1\) as \(\frac{y}{y}\):
\[ \frac{a}{b} = \frac{y}{y} - \frac{x}{y} \]
Now, combine the fractions:
\[ \frac{a}{b} = \frac{y - x}{y} \]

### Step 3: Cross-multiply
Next, we can cross-multiply to express \(a\) in terms of \(b\):
\[ a \cdot y = b \cdot (y - x) \]

### Step 4: Rearranging for \(\frac{b}{a}\)
To find \(\frac{b}{a}\), we can take the reciprocal of \(\frac{a}{b}\):
\[ \frac{b}{a} = \frac{y}{y - x} \]

### Final Result
Thus, the value of \(\frac{b}{a}\) is:
\[ \frac{b}{a} = \frac{y}{y - x} \]