Understanding Ratios
To find the ratio A:B:C based on the given ratios A:B and B:C, we need to express all terms in relation to a common variable.
Given Ratios
- A:B = 3:5
- B:C = 10:13
Finding the Common Term (B)
1. From the ratio A:B = 3:5, we can express A and B as:
- A = 3x
- B = 5x
2. From the ratio B:C = 10:13, we can express B and C as:
- B = 10y
- C = 13y
Equating B Values
Since both expressions represent B, we can set them equal to each other:
- 5x = 10y
Solving for x in terms of y
1. Dividing both sides by 5:
- x = 2y
Substituting Back to Find A and C
1. Substitute x back into the expressions for A and C:
- A = 3x = 3(2y) = 6y
- B = 10y (from the second ratio)
- C = 13y (from the second ratio)
Final Ratios
Now we can express A, B, and C in terms of y:
- A = 6y
- B = 10y
- C = 13y
Thus, the combined ratio A:B:C is:
- A:B:C = 6y:10y:13y
Conclusion
The final ratio A:B:C simplifies to:
- A:B:C = 6:10:13
This gives us the desired relationship among A, B, and C.

A:B = 3:5 & B:C = 10:13

In A:B = 3:5 multiply by 2

A:B = 6:10

So, Comparing A:B & B:C

A : B : C : = 6 : 10 : 13 ( Ans )