If `a : b : c = 7 : 3 : 5`, then `(a+ b + c): (2a+ b- c)` is equal to

Options

A. `1:2`
B. `2:3`
C. `3:4`
D. `5:4`

Answer

To solve the problem, we start with the given ratio \( a : b : c = 7 : 3 : 5 \). We can express \( a \), \( b \), and \( c \) in terms of a common variable \( x \).

### Step 1: Express \( a \), \( b \), and \( c \) in terms of \( x \)
Let:
- \( a = 7x \)
- \( b = 3x \)
- \( c = 5x \)

### Step 2: Calculate \( a + b + c \)
Now, we find \( a + b + c \):
\[ a + b + c = 7x + 3x + 5x = 15x \]

### Step 3: Calculate \( 2a + b - c \)
Next, we calculate \( 2a + b - c \):
\[ 2a + b - c = 2(7x) + 3x - 5x \]
\[ = 14x + 3x - 5x = 12x \]

### Step 4: Form the ratio \( (a + b + c) : (2a + b - c) \)
Now we can form the ratio:
\[ (a + b + c) : (2a + b - c) = 15x : 12x \]

### Step 5: Simplify the ratio
We can simplify the ratio \( 15x : 12x \) by dividing both terms by \( 3x \):
\[ = \frac{15x}{3x} : \frac{12x}{3x} = 5 : 4 \]

### Final Answer
Thus, the ratio \( (a + b + c) : (2a + b - c) \) is equal to \( 5 : 4 \).

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