If a :b =3: 5 andb: c =4: 7, then a : c is equal to

Options

A. `11 : 35`
B. `35 : 11`
C. `35 : 12`
D. `12 : 35`

Answer

To solve the problem where \( a : b = 3 : 5 \) and \( b : c = 4 : 7 \), we need to find the ratio \( a : c \).

### Step-by-Step Solution:

1. **Express the Ratios in Fraction Form**:
- From the ratio \( a : b = 3 : 5 \), we can express it as:
\[ \frac{a}{b} = \frac{3}{5} \]
- From the ratio \( b : c = 4 : 7 \), we can express it as:
\[ \frac{b}{c} = \frac{4}{7} \]

2. **Find the Value of \( b \)**:
- To find a common value for \( b \) in both ratios, we can express \( b \) in terms of a common factor. Let’s denote \( b = 20 \) (the least common multiple of 5 and 4).
- From \( a : b = 3 : 5 \):
\[ \frac{a}{20} = \frac{3}{5} \implies a = 20 \times \frac{3}{5} = 12 \]
- From \( b : c = 4 : 7 \):
\[ \frac{20}{c} = \frac{4}{7} \implies c = 20 \times \frac{7}{4} = 35 \]

3. **Write the Ratio \( a : c \)**:
- Now we have \( a = 12 \) and \( c = 35 \).
- Therefore, the ratio \( a : c \) can be written as:
\[ a : c = 12 : 35 \]

4. **Final Answer**:
- The ratio \( a : c \) is equal to \( 12 : 35 \).