If `(1)/(a):(1)/(b):(1)/(c )` =4:6:10 then the value of a:b:c is

Options

A. `10:6:7`
B. `7:6:4`
C. `11:10:12`
D. `15:10:6`

Answer

To solve the problem, we start with the given ratio:

\[ \frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 4 : 6 : 10 \]

### Step 1: Simplify the Ratio
First, we simplify the ratio \(4 : 6 : 10\) by dividing each term by 2:

\[ \frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 2 : 3 : 5 \]

### Step 2: Assign Variables
Let’s assign variables to each part of the ratio:

\[ \frac{1}{a} = 2x, \quad \frac{1}{b} = 3x, \quad \frac{1}{c} = 5x \]

### Step 3: Express \(a\), \(b\), and \(c\)
Now, we can express \(a\), \(b\), and \(c\) in terms of \(x\):

\[ a = \frac{1}{2x}, \quad b = \frac{1}{3x}, \quad c = \frac{1}{5x} \]

### Step 4: Find the Ratio \(a : b : c\)
Now we need to find the ratio \(a : b : c\):

\[ a : b : c = \frac{1}{2x} : \frac{1}{3x} : \frac{1}{5x} \]

### Step 5: Eliminate \(x\)
Since \(x\) is common in all terms, we can eliminate it:

\[ a : b : c = \frac{1}{2} : \frac{1}{3} : \frac{1}{5} \]

### Step 6: Convert to a Common Denominator
To express this ratio in a simpler form, we can find the least common multiple (LCM) of the denominators 2, 3, and 5, which is 30. Now we multiply each term by 30:

\[ a : b : c = 30 \cdot \frac{1}{2} : 30 \cdot \frac{1}{3} : 30 \cdot \frac{1}{5} \]

This simplifies to:

\[ a : b : c = 15 : 10 : 6 \]

### Conclusion
Thus, the final ratio \(a : b : c\) is:

\[ \boxed{15 : 10 : 6} \]