A shopkeeper bought rice worth Rs 4,500. He sold one-third of it at 10% profit. If he desires a profit of 12% on the whole, find :
the percentage profit on the rest of the rice.

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Determine the total cost price (CP)
The total cost price of the rice is given as Rs 4,500.

### Step 2: Calculate the cost price of one-third of the rice
The cost price of one-third of the rice (CP1) can be calculated as:
\[ CP1 = \frac{1}{3} \times 4500 = 1500 \]

### Step 3: Calculate the cost price of the remaining two-thirds of the rice
The cost price of the remaining two-thirds of the rice (CP2) can be calculated as:
\[ CP2 = \frac{2}{3} \times 4500 = 3000 \]

### Step 4: Calculate the profit from selling one-third of the rice at 10% profit
The profit (P1) from selling one-third of the rice at a 10% profit can be calculated as:
\[ P1 = 10\% \text{ of } CP1 = \frac{10}{100} \times 1500 = 150 \]

### Step 5: Calculate the selling price of one-third of the rice
The selling price (SP1) of the one-third of the rice can be calculated as:
\[ SP1 = CP1 + P1 = 1500 + 150 = 1650 \]

### Step 6: Determine the desired net profit on the whole rice
The shopkeeper desires a net profit of 12% on the total cost price. Therefore, the net profit (P_net) can be calculated as:
\[ P_{net} = 12\% \text{ of } 4500 = \frac{12}{100} \times 4500 = 540 \]

### Step 7: Calculate the profit from selling the remaining rice
Let the profit from selling the remaining rice (P2) be calculated at x% profit. The profit from selling the remaining rice can be expressed as:
\[ P2 = \frac{x}{100} \times CP2 = \frac{x}{100} \times 3000 = 30x \]

### Step 8: Set up the equation for total profit
The total profit from both sales must equal the desired net profit:
\[ P1 + P2 = P_{net} \]
Substituting the values we have:
\[ 150 + 30x = 540 \]

### Step 9: Solve for x
Rearranging the equation gives:
\[ 30x = 540 - 150 \]
\[ 30x = 390 \]
Dividing both sides by 30 gives:
\[ x = \frac{390}{30} = 13 \]

### Step 10: Conclusion
The percentage profit on the remaining rice is **13%**.

---