Givne `(x)/(y)=(5)/(6)`
now x is reduced by 62 and the ratio of x and y becomes `(2)/(3)` then find x and y respectively :-

Options

A. 310, 372
B. 392, 330
C. 500, 600
D. 250, 300

Answer

To solve the problem step by step, we will use the information given in the question.

### Step 1: Write the initial ratio
We are given that:
\[ \frac{x}{y} = \frac{5}{6} \]
From this, we can express \(x\) in terms of \(y\):
\[ x = \frac{5}{6}y \quad \text{(Equation 1)} \]

### Step 2: Set up the new ratio after reducing \(x\)
When \(x\) is reduced by 62, the new ratio of \(x\) and \(y\) becomes:
\[ \frac{x - 62}{y} = \frac{2}{3} \]
From this, we can express \(x - 62\) in terms of \(y\):
\[ x - 62 = \frac{2}{3}y \quad \text{(Equation 2)} \]

### Step 3: Substitute \(x\) from Equation 1 into Equation 2
Now, we will substitute the value of \(x\) from Equation 1 into Equation 2:
\[ \frac{5}{6}y - 62 = \frac{2}{3}y \]

### Step 4: Clear the fractions
To eliminate the fractions, we can multiply the entire equation by 6 (the least common multiple of the denominators):
\[ 6\left(\frac{5}{6}y - 62\right) = 6\left(\frac{2}{3}y\right) \]
This simplifies to:
\[ 5y - 372 = 4y \]

### Step 5: Solve for \(y\)
Now, we can isolate \(y\):
\[ 5y - 4y = 372 \]
\[ y = 372 \]

### Step 6: Substitute \(y\) back to find \(x\)
Now that we have \(y\), we can substitute it back into Equation 1 to find \(x\):
\[ x = \frac{5}{6} \times 372 \]
Calculating this gives:
\[ x = 310 \]

### Final Answer
Thus, the values of \(x\) and \(y\) are:
\[ x = 310, \quad y = 372 \]