`A:B=2:3`, `B:C=3:4`, `C:D=4:5`
Find `A:B:C:D=?`

Answer

To find the combined ratio of A:B:C:D given the ratios A:B = 2:3, B:C = 3:4, and C:D = 4:5, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A:B = 2:3
- B:C = 3:4
- C:D = 4:5

### Step 2: Express each variable in terms of a common variable
Let's express A, B, C, and D in terms of a common variable.

From A:B = 2:3, we can write:
- A = 2x
- B = 3x

From B:C = 3:4, we can write:
- B = 3y
- C = 4y

Since B is common in both ratios, we can equate the two expressions for B:
3x = 3y
This implies that x = y.

### Step 3: Substitute y back into the equations
Now we can express C in terms of x:
- C = 4y = 4x

From C:D = 4:5, we can write:
- C = 4z
- D = 5z

Again, since C is common, we equate the two expressions for C:
4x = 4z
This implies that x = z.

### Step 4: Substitute z back into the equations
Now we can express D in terms of x:
- D = 5z = 5x

### Step 5: Write down all variables in terms of x
Now we have:
- A = 2x
- B = 3x
- C = 4x
- D = 5x

### Step 6: Combine the ratios
Now we can express the combined ratio A:B:C:D:
- A:B:C:D = 2x : 3x : 4x : 5x

### Step 7: Simplify the ratio
Since x is common in all terms, we can simplify the ratio:
- A:B:C:D = 2 : 3 : 4 : 5

### Final Answer
Thus, the combined ratio A:B:C:D is **2:3:4:5**.

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