Question

If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is:

• A. 10 : 12 : 11
• B. 11 : 13 : 12
• C. 11 : 13 : 12
• D. 19 : 21 : 20

Answer 1

The Correct Option is B

To solve the problem, we need to find A + B : B + C : A + C given the ratios A : B = 5 : 6 and B : C = 6 : 7. 

First, let's express A, B, and C in terms of a common variable to make calculations easy. Assume B = 6x. Then:

• Since A : B = 5 : 6, A = 5x.
• Since B : C = 6 : 7, C = 7x.

Now, calculate each part of the desired ratio:

• A + B = 5x + 6x = 11x
• B + C = 6x + 7x = 13x
• A + C = 5x + 7x = 12x

Therefore, the ratio A + B : B + C : A + C is:

• 11x : 13x : 12x

This can be simplified to:

• 11 : 13 : 12

The correct answer is 11 : 13 : 12.

Answer 2

Let's solve this problem step by step:

1. Given Ratios:

• A : B = 5 : 6
• B : C = 6 : 7

2. Combine Ratios:

• Since B is common in both ratios and its value is the same (6), we can directly combine the ratios:
• A : B : C = 5 : 6 : 7

3. Calculate A + B, B + C, and A + C:

• A + B = 5 + 6 = 11
• B + C = 6 + 7 = 13
• A + C = 5 + 7 = 12

4. Express the Required Ratio:

• A + B : B + C : A + C = 11 : 13 : 12

Therefore, A + B  B + C: A + C is 11: 13: 2.

The correct answer is Option 2.