In a rehabitation programe, a group of 50 families were assured new houses and compensation by the government . Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new house is 6 greater than the number of families who got compensation. How many families got houses?

Options

A. 22
B. 28
C. 23
D. 25

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given.

### Step 1: Define the Variables
Let:
- \( y \) = number of families who got compensation
- \( x \) = number of families who got both houses and compensation
- The number of families who got houses = \( y + 6 \) (since it is stated that the number of families who got houses is 6 greater than those who got compensation)

### Step 2: Set Up the Equation
According to the problem, the total number of families is 50. We can express this as:
\[ x + y + (y + 6) + x = 50 \]
This simplifies to:
\[ 2x + 2y + 6 = 50 \]

### Step 3: Simplify the Equation
Subtract 6 from both sides:
\[ 2x + 2y = 44 \]
Now, divide the entire equation by 2:
\[ x + y = 22 \]

### Step 4: Express the Number of Families Who Got Houses
The total number of families who got houses can be expressed as:
\[ \text{Number of families who got houses} = x + (y + 6) = x + y + 6 \]
Substituting \( x + y \) from the previous step:
\[ \text{Number of families who got houses} = 22 + 6 = 28 \]

### Conclusion
Thus, the number of families who got houses is **28**.

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