"Help India Foundation" and "People for People Organisation" decided to distribute the blankets among 22 men and 28 women who are Tsunami victims. When HIF and PPO distributed their respective blankets evenly among 28 women they were left with 24 and 16 blankets respectively. If they distributed their blankets evenly among 22 men they were left with 12 blankets each. So finally they decided to combine all their blankets and then distributed among 22 men and 28 women altogether then no any blanket remained undistributed . Minimum total blankets distributed by them were:

Options

A. 960
B. 700
C. 1300
D. none of these

Answer

To solve the problem, we need to determine the minimum total number of blankets distributed by the Help India Foundation (HIF) and the People for People Organisation (PPO) based on the given conditions.

### Step-by-Step Solution:

1. **Understanding the Distribution Conditions**:
- When HIF distributes blankets among 28 women, they are left with 24 blankets.
- When PPO distributes blankets among 28 women, they are left with 16 blankets.
- When HIF distributes blankets among 22 men, they are left with 12 blankets.
- When PPO distributes blankets among 22 men, they are left with 12 blankets.

2. **Setting Up Equations**:
- Let \( M \) be the total number of blankets with HIF.
- Let \( N \) be the total number of blankets with PPO.

From the conditions, we can derive the following equations:
- For HIF (when distributed among women):
\[ M = 28k + 24 \quad (1) \]
- For PPO (when distributed among women):
\[ N = 28l + 16 \quad (2) \]
- For HIF (when distributed among men):
\[ M = 22a + 12 \quad (3) \]
- For PPO (when distributed among men):
\[ N = 22b + 12 \quad (4) \]

3. **Equating the Equations**:
- From equations (1) and (3):
\[ 28k + 24 = 22a + 12 \]
Rearranging gives:
\[ 28k - 22a = -12 \quad (5) \]
- From equations (2) and (4):
\[ 28l + 16 = 22b + 12 \]
Rearranging gives:
\[ 28l - 22b = -4 \quad (6) \]

4. **Finding the Least Values**:
- For equation (5), we can express it as:
\[ 28k - 22a = -12 \implies 14k - 11a = -6 \]
- For equation (6), we can express it as:
\[ 28l - 22b = -4 \implies 14l - 11b = -2 \]

5. **Finding Integer Solutions**:
- To find integer solutions for \( k \) and \( a \) from (5), we can test small values for \( k \) and find corresponding \( a \).
- Similarly, for (6), we can test small values for \( l \) and find corresponding \( b \).

6. **Calculating the Minimum Total Blankets**:
- After finding suitable values for \( M \) and \( N \) from the equations, we can find the total number of blankets:
\[ M + N \]
- We need to ensure that \( M + N \) is divisible by the total number of people (50).

7. **Final Calculation**:
- After testing various combinations, we find that the minimum total number of blankets \( M + N \) that satisfies all conditions and is divisible by 50 is 1300.

### Conclusion:
The minimum total blankets distributed by Help India Foundation and People for People Organisation is **1300**.