If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is:
- 10 : 12 : 11
11 : 13 : 12
11 : 13 : 12
- 19 : 21 : 20
The Correct Option is B
Approach Solution - 1
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.
Approach Solution -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.
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