If `a/3 = b/5 = c/7`, then value of `(a+ b+c)/b` will be:

Options

A. 7
B. 3
C. 10
D. 5

Answer

To solve the equation \( \frac{a}{3} = \frac{b}{5} = \frac{c}{7} \) and find the value of \( \frac{a + b + c}{b} \), we can follow these steps:

### Step 1: Set a common variable
Let \( k \) be the common value such that:
\[ \frac{a}{3} = \frac{b}{5} = \frac{c}{7} = k \]

### Step 2: Express \( a \), \( b \), and \( c \) in terms of \( k \)
From the equations, we can express \( a \), \( b \), and \( c \) as:
\[ a = 3k \]
\[ b = 5k \]
\[ c = 7k \]

### Step 3: Substitute \( a \), \( b \), and \( c \) into \( a + b + c \)
Now, we can find \( a + b + c \):
\[ a + b + c = 3k + 5k + 7k = (3 + 5 + 7)k = 15k \]

### Step 4: Substitute into the expression \( \frac{a + b + c}{b} \)
Now, we substitute \( a + b + c \) and \( b \) into the expression:
\[ \frac{a + b + c}{b} = \frac{15k}{5k} \]

### Step 5: Simplify the expression
We can simplify the fraction:
\[ \frac{15k}{5k} = \frac{15}{5} = 3 \]

### Final Answer
Thus, the value of \( \frac{a + b + c}{b} \) is:
\[ \boxed{3} \]