When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percent, if the commission is reduced to 24%.

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the given information
- The producer allows a 36% commission on the retail price (RP) and earns a profit of 8.8%.
- We need to find the profit percentage if the commission is reduced to 24%.

### Step 2: Set the retail price (RP)
Assume the retail price (RP) is 100.

### Step 3: Calculate the selling price (SP) with 36% commission
- The commission is 36% of RP, which means:
\[ \text{Commission} = 36\% \text{ of } 100 = 36 \]
- Therefore, the selling price (SP) after the commission is:
\[ SP = RP - \text{Commission} = 100 - 36 = 64 \]

### Step 4: Relate SP to the cost price (CP) using profit percentage
- The profit is given as 8.8%, which means:
\[ SP = CP + 8.8\% \text{ of } CP = 108.8\% \text{ of } CP \]
- This can be expressed as:
\[ SP = 1.088 \times CP \]
- We know SP is 64, so:
\[ 64 = 1.088 \times CP \]

### Step 5: Calculate the cost price (CP)
- Rearranging the equation to find CP:
\[ CP = \frac{64}{1.088} \]
- Calculating CP:
\[ CP \approx 58.8 \]

### Step 6: Calculate the new selling price (SP) with 24% commission
- Now, if the commission is reduced to 24%, the new selling price is:
\[ \text{New Commission} = 24\% \text{ of } 100 = 24 \]
- Therefore, the new selling price (SP) is:
\[ SP = RP - \text{New Commission} = 100 - 24 = 76 \]

### Step 7: Calculate the profit with the new selling price
- The profit can be calculated as:
\[ \text{Profit} = SP - CP = 76 - 58.8 = 17.2 \]

### Step 8: Calculate the profit percentage
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
- Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{17.2}{58.8}\right) \times 100 \approx 29.2\% \]

### Final Answer
The profit percentage when the commission is reduced to 24% is approximately **29.2%**.

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