To solve the problem step by step, we will first establish the relationships between the shares of P, Q, and R based on the given conditions.
### Step 1: Establish the ratios based on the problem statement
- For every 1 rupee that P gets, Q gets 75 paise.
- For every 1 rupee that Q gets, R gets 50 paise.
Let's convert these amounts into a common unit (paisa):
- 1 rupee = 100 paise
- Therefore, if P gets 100 paise, Q gets 75 paise.
- If Q gets 100 paise, R gets 50 paise.
### Step 2: Express Q's share in terms of P's share
If P gets 100 paise, then:
- Q's share = 75 paise
- R's share (when Q gets 75 paise) can be calculated as follows:
- Q's share = 75 paise, which is \( \frac{75}{100} \) of a rupee.
- R's share for every rupee Q gets is 50 paise, so R gets:
\[
R's\ share = 75 \times \frac{50}{100} = 37.5\ paise
\]
### Step 3: Establish the ratio of shares
From the above, we can establish the ratio of shares of P, Q, and R:
- P's share = 100 paise
- Q's share = 75 paise
- R's share = 37.5 paise
To simplify, we can multiply all shares by 2 to eliminate the decimal:
- P's share = 200 paise
- Q's share = 150 paise
- R's share = 75 paise
Thus, the ratio of P:Q:R = 200:150:75, which simplifies to:
\[
P:Q:R = 8:6:3
\]
### Step 4: Calculate the total parts
Now, we can find the total parts in the ratio:
\[
Total\ parts = 8 + 6 + 3 = 17
\]
### Step 5: Use R's share to find the total sum
We know that R's share is Rs 36. Since R's share corresponds to 3 parts in the ratio:
\[
\frac{3}{17} \times Total\ Sum = 36
\]
Let \( Total\ Sum = S \):
\[
\frac{3}{17} S = 36
\]
To find S, we can rearrange:
\[
S = 36 \times \frac{17}{3} = 36 \times \frac{17}{3} = 12 \times 17 = 204
\]
### Step 6: Find P's share
Now that we have the total sum, we can find P's share:
\[
P's\ share = \frac{8}{17} \times S = \frac{8}{17} \times 204
\]
Calculating this gives:
\[
P's\ share = \frac{8 \times 204}{17} = \frac{1632}{17} = 96
\]
### Final Answer
Thus, the share of P is Rs 96.
