The average earning of each member of the Ambani family is 20% less than the average earning of each member of the Sahara family and the total earning of Ambani's family is 20% more than the total earning of Saharas's family. The no of family members in the Sahara is what percent of the no of family members of Ambani

Options

A. `25%`
B. `20%`
C. `66.66%`
D. none of these

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided in the question.

### Step 1: Define Variables
Let:
- \( A \) = Number of members in the Ambani family
- \( S \) = Number of members in the Sahara family
- \( E_A \) = Average earning per member of the Ambani family
- \( E_S \) = Average earning per member of the Sahara family

### Step 2: Establish Relationships
According to the problem:
1. The average earning of each member of the Ambani family is 20% less than that of the Sahara family:
\[ E_A = E_S - 0.2E_S = 0.8E_S \]

2. The total earning of the Ambani family is 20% more than that of the Sahara family:
\[ \text{Total earning of Ambani} = A \cdot E_A \]
\[ \text{Total earning of Sahara} = S \cdot E_S \]
\[ A \cdot E_A = 1.2 \cdot (S \cdot E_S) \]

### Step 3: Substitute the Average Earnings
Substituting \( E_A \) in the total earning equation:
\[ A \cdot (0.8E_S) = 1.2 \cdot (S \cdot E_S) \]

### Step 4: Simplify the Equation
We can cancel \( E_S \) from both sides (assuming \( E_S \neq 0 \)):
\[ 0.8A = 1.2S \]

### Step 5: Rearranging the Equation
Rearranging gives:
\[ \frac{A}{S} = \frac{1.2}{0.8} = \frac{12}{8} = \frac{3}{2} \]

### Step 6: Find the Percentage
Now, we need to find what percentage the number of members in the Sahara family is of the number of members in the Ambani family:
\[ \frac{S}{A} = \frac{2}{3} \]
To express this as a percentage:
\[ \frac{S}{A} \times 100 = \frac{2}{3} \times 100 = 66.67\% \]

### Final Answer
The number of family members in the Sahara family is **66.67%** of the number of family members in the Ambani family.

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