Find the compound ratio of 2 : 7, 5 : 3 and 4 : 7

Options

A. `147 : 40`
B. `40 : 147`
C. `147 : 30 `
D. `30 :147`

Answer

To find the compound ratio of the ratios 2:7, 5:3, and 4:7, we will follow these steps:

### Step 1: Identify the Ratios
We have three ratios:
- A : B = 2 : 7
- C : D = 5 : 3
- E : F = 4 : 7

### Step 2: Write Down the Formula for Compound Ratio
The formula for the compound ratio of the ratios A : B, C : D, and E : F is given by:
\[ \text{Compound Ratio} = \frac{A \times C \times E}{B \times D \times F} \]

### Step 3: Substitute the Values into the Formula
Substituting the values from the ratios:
- A = 2, B = 7
- C = 5, D = 3
- E = 4, F = 7

We get:
\[ \text{Compound Ratio} = \frac{2 \times 5 \times 4}{7 \times 3 \times 7} \]

### Step 4: Calculate the Numerator
Calculating the numerator:
\[ 2 \times 5 = 10 \]
\[ 10 \times 4 = 40 \]
So, the numerator is 40.

### Step 5: Calculate the Denominator
Calculating the denominator:
\[ 7 \times 3 = 21 \]
\[ 21 \times 7 = 147 \]
So, the denominator is 147.

### Step 6: Combine the Results
Now, we can combine the results:
\[ \text{Compound Ratio} = \frac{40}{147} \]

### Final Answer
Thus, the compound ratio of 2:7, 5:3, and 4:7 is:
\[ \frac{40}{147} \]

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