In a ratio which is equal to 5:8 if the antecedent is 40 then consequent is

Options

A. 25
B. 64
C. 48
D. none of these

Answer

To find the consequent in the ratio of 5:8 when the antecedent is 40, we can follow these steps:

### Step 1: Understand the Ratio
The ratio 5:8 means that for every 5 parts of the antecedent, there are 8 parts of the consequent.

### Step 2: Set Up the Proportion
Let the antecedent be represented as \( a \) and the consequent as \( b \). According to the given ratio:
\[ \frac{a}{b} = \frac{5}{8} \]

### Step 3: Substitute the Antecedent
We know the antecedent \( a \) is 40. Substitute this value into the proportion:
\[ \frac{40}{b} = \frac{5}{8} \]

### Step 4: Cross-Multiply
To solve for \( b \), we can cross-multiply:
\[ 40 \cdot 8 = 5 \cdot b \]

### Step 5: Calculate
Now, calculate the left side:
\[ 320 = 5b \]

### Step 6: Solve for \( b \)
To find \( b \), divide both sides by 5:
\[ b = \frac{320}{5} = 64 \]

### Conclusion
The consequent is 64.