"Help India Foundation" and "People for People Organization" 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 . In the above problem the ratio of blankets between HIF and PPO is :

Options

A. `43/157`
B. `147/179`
C. `59/101`
D. can't be determined

Answer

To solve the problem, we need to determine the ratio of blankets between the "Help India Foundation" (HIF) and the "People for People Organization" (PPO). Let's denote the number of blankets with HIF as \( M \) and with PPO as \( N \).

### Step 1: Set Up the Equations
From the problem, we know the following:

1. When HIF distributes \( M \) blankets among 28 women, they are left with 24 blankets.
This can be expressed as:
\[ M = 28k + 24 \quad \text{(for some integer } k\text{)} \]

2. When HIF distributes \( M \) blankets among 22 men, they are left with 12 blankets.
This can be expressed as:
\[ M = 22m + 12 \quad \text{(for some integer } m\text{)} \]

3. When PPO distributes \( N \) blankets among 28 women, they are left with 16 blankets.
This can be expressed as:
\[ N = 28p + 16 \quad \text{(for some integer } p\text{)} \]

4. When PPO distributes \( N \) blankets among 22 men, they are left with 12 blankets.
This can be expressed as:
\[ N = 22q + 12 \quad \text{(for some integer } q\text{)} \]

### Step 2: Rearranging the Equations
From the equations, we can rearrange them:

For HIF:
- From \( M = 28k + 24 \):
\[ M - 24 = 28k \quad \Rightarrow \quad M \equiv 24 \mod 28 \]

- From \( M = 22m + 12 \):
\[ M - 12 = 22m \quad \Rightarrow \quad M \equiv 12 \mod 22 \]

For PPO:
- From \( N = 28p + 16 \):
\[ N - 16 = 28p \quad \Rightarrow \quad N \equiv 16 \mod 28 \]

- From \( N = 22q + 12 \):
\[ N - 12 = 22q \quad \Rightarrow \quad N \equiv 12 \mod 22 \]

### Step 3: Solving the Congruences
Now we need to solve the congruences for \( M \) and \( N \).

#### For \( M \):
1. \( M \equiv 24 \mod 28 \)
2. \( M \equiv 12 \mod 22 \)

Using the method of substitution or the Chinese Remainder Theorem, we can find a common solution for \( M \).

#### For \( N \):
1. \( N \equiv 16 \mod 28 \)
2. \( N \equiv 12 \mod 22 \)

Similarly, we can find a common solution for \( N \).

### Step 4: Finding the Ratio
Once we have the values of \( M \) and \( N \), we can find the ratio \( \frac{M}{N} \).

### Conclusion
However, as noted in the video transcript, without specific values for \( k, m, p, \) and \( q \), we cannot determine a fixed ratio between \( M \) and \( N \). Thus, the ratio of blankets between HIF and PPO cannot be determined.