If `a/b=7/9,b/c=3/5`, then the value of `a:b:c` is

Options

A. `7:3:15`
B. `21:27:42`
C. `7:9:15`
D. `7:9:5`

Answer

To find the value of \( a:b:c \) given that \( \frac{a}{b} = \frac{7}{9} \) and \( \frac{b}{c} = \frac{3}{5} \), we can follow these steps:

### Step-by-Step Solution:

1. **Express \( a \) in terms of \( b \)**:
From the first ratio \( \frac{a}{b} = \frac{7}{9} \), we can express \( a \) as:
\[ a = \frac{7}{9}b \]

2. **Express \( b \) in terms of \( c \)**:
From the second ratio \( \frac{b}{c} = \frac{3}{5} \), we can express \( b \) as:
\[ b = \frac{3}{5}c \]

3. **Substitute \( b \) in the equation for \( a \)**:
Now, substitute \( b = \frac{3}{5}c \) into the equation for \( a \):
\[ a = \frac{7}{9} \left(\frac{3}{5}c\right) = \frac{7 \times 3}{9 \times 5}c = \frac{21}{45}c \]

4. **Simplify \( a \)**:
We can simplify \( \frac{21}{45} \):
\[ \frac{21}{45} = \frac{7}{15} \]
Thus, we have:
\[ a = \frac{7}{15}c \]

5. **Now express \( a, b, c \) in terms of a common variable**:
Let \( c = 15k \) for some variable \( k \). Then:
\[ b = \frac{3}{5}c = \frac{3}{5}(15k) = 9k \]
\[ a = \frac{7}{15}c = \frac{7}{15}(15k) = 7k \]

6. **Write the ratios \( a:b:c \)**:
Now we can express the ratios:
\[ a:b:c = 7k : 9k : 15k \]
Since \( k \) is a common factor, we can simplify this to:
\[ a:b:c = 7 : 9 : 15 \]

### Final Result:
Thus, the value of \( a:b:c \) is \( 7:9:15 \).