A merchant has 2000 kg of rice, one part of which he sells at 36%profit and the rest at 16% profit.He gains 28% on the whole.Find the quantity sold at 16%.

Options

A. 400 kg
B. 300 kg
C. 900 kg
D. 800 kg

Answer

To solve the problem step by step, we will use the concept of alligation to find the quantity of rice sold at 16% profit.

### Step 1: Understand the given information
We have:
- Total quantity of rice = 2000 kg
- Profit from one part = 36%
- Profit from the other part = 16%
- Overall profit = 28%

### Step 2: Set up the alligation
We can set up the alligation to find the ratio of quantities sold at different profits. The formula for alligation is:

\[ \text{Profit of higher part} - \text{Overall profit} : \text{Overall profit} - \text{Profit of lower part} \]

Substituting the values we have:
- Profit of higher part (36%) = 36
- Overall profit (28%) = 28
- Profit of lower part (16%) = 16

So, we calculate:
\[ \text{Difference 1} = 36 - 28 = 8 \]
\[ \text{Difference 2} = 28 - 16 = 12 \]

### Step 3: Establish the ratio
Now, we can establish the ratio of the quantities sold at 36% profit and 16% profit:
\[ \text{Ratio} = 8 : 12 = 2 : 3 \]

### Step 4: Calculate the quantities
Let the quantity sold at 36% profit be \(2x\) and the quantity sold at 16% profit be \(3x\). Since the total quantity of rice is 2000 kg, we can write the equation:
\[ 2x + 3x = 2000 \]
\[ 5x = 2000 \]
\[ x = \frac{2000}{5} = 400 \]

### Step 5: Find the quantity sold at 16%
Now, we can find the quantity sold at 16% profit:
\[ \text{Quantity sold at 16%} = 3x = 3 \times 400 = 1200 \text{ kg} \]

### Conclusion
Thus, the quantity sold at 16% profit is **1200 kg**.