Some quantity of rice is required for each member of a family of 15 members. On a particular day, due to the absence of some members of the family, the consumption of rice was reduced in the ratio 5 : 3. Find the number of members absent on that day.

Options

A. 3
B. 6
C. 8
D. 9

Answer

To solve the problem, we need to determine the number of family members who were absent based on the given ratio of rice consumption.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The family consists of 15 members.
- The consumption of rice was reduced in the ratio of 5:3 due to the absence of some members.

2. **Set Up the Ratios**:
- Let the total rice consumption for 15 members be represented as 5 units (before the absence).
- When some members are absent, the consumption reduces to 3 units.

3. **Determine the Consumption per Member**:
- Since 5 units of rice are consumed by 15 members, we can find the consumption per member:
\[ \text{Consumption per member} = \frac{5 \text{ units}}{15 \text{ members}} = \frac{1}{3} \text{ units per member} \]

4. **Calculate the Number of Members Consuming Rice After Absences**:
- Let \( x \) be the number of members present on that day. Therefore, the consumption after some members are absent can be expressed as:
\[ \text{Consumption for } x \text{ members} = \frac{1}{3} \times x \text{ units} \]

5. **Set Up the Equation Based on the Ratio**:
- According to the problem, the consumption after the absence is represented by 3 units. Thus, we can set up the equation:
\[ \frac{1}{3} \times x = 3 \]

6. **Solve for \( x \)**:
- To find \( x \), multiply both sides of the equation by 3:
\[ x = 3 \times 3 = 9 \text{ members} \]

7. **Determine the Number of Members Absent**:
- The number of members absent can be calculated by subtracting the number of members present from the total number of members:
\[ \text{Members absent} = 15 - x = 15 - 9 = 6 \]

### Final Answer:
The number of members absent on that day is **6**.