Question

If\(A : B = 6 : 13 \text{ and } B : C = 2 : 7\),then what is the value of\(A : B : C?\)

• A. \(12 : 91 : 26\)
• B. \(12 : 26 : 91\)
• C. \(78 : 26 : 91\)
• D. \(12 : 26 : 42\)

Answer 1

The Correct Option is B

Finding the Ratio A : B : C 

Given Ratios:

• \( A : B = 6 : 13 \)
• \( B : C = 2 : 7 \)

Step 1: Express \( B \) in a Common Term

From the first ratio, let \( B = 13k \) and from the second ratio, let \( B = 2m \).

Step 2: Find the LCM of 13 and 2

The least common multiple (LCM) of 13 and 2 is 26.

Step 3: Adjust the Ratios

• Multiply the first ratio by 2 to make \( B = 26 \): \[ A : B = (6 \times 2) : (13 \times 2) = 12 : 26 \]
• Multiply the second ratio by 13 to make \( B = 26 \): \[ B : C = (2 \times 13) : (7 \times 13) = 26 : 91 \]

Step 4: Final Ratio

Now, combining both adjusted ratios:

\[ A : B : C = 12 : 26 : 91 \]

Final Answer:

Thus, the final ratio is 12:26:91 (Option B).