If A:B =4:5 and B:C=20: 11, then find A:B:C ?

Options

A. `4:20:7`
B. `16:25:22`
C. `16:20:11`
D. `8:10:7`

Answer

To find the ratio A:B:C given the ratios A:B = 4:5 and B:C = 20:11, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A:B = 4:5
- B:C = 20:11

### Step 2: Express the ratios in terms of a common variable
Let’s express A and B in terms of a common variable. From A:B = 4:5, we can write:
- A = 4x
- B = 5x

### Step 3: Express B in terms of C
From B:C = 20:11, we can express B and C in terms of another variable. Let’s denote this variable as y:
- B = 20y
- C = 11y

### Step 4: Equate the two expressions for B
Since B is common in both ratios, we can set the two expressions for B equal to each other:
- 5x = 20y

### Step 5: Solve for x in terms of y
To find x in terms of y, divide both sides by 5:
- x = 4y

### Step 6: Substitute x back to find A and B
Now substitute x back into the expressions for A and B:
- A = 4x = 4(4y) = 16y
- B = 5x = 5(4y) = 20y

### Step 7: Write down the expressions for A, B, and C
Now we have:
- A = 16y
- B = 20y
- C = 11y

### Step 8: Write the combined ratio A:B:C
Now we can write the combined ratio:
- A:B:C = 16y : 20y : 11y

### Step 9: Simplify the ratio
Since y is a common factor, we can simplify the ratio:
- A:B:C = 16 : 20 : 11

### Final Answer
Thus, the final ratio A:B:C is:
**16:20:11**

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