To solve the problem step by step, we need to analyze the statements given and derive the necessary information to find out the profit earned by the shopkeeper in November 2016.
### Step 1: Define Variables
Let:
- Profit in October 2016 = \( X \)
- Profit in November 2016 = \( Y \)
- Profit in December 2016 = \( Z \)
### Step 2: Analyze the Statements
1. **From Statement 1**: "He earned 40% more profit in December 2016 as compared to October 2016."
- This means:
\[
Z = X + 0.4X = 1.4X
\]
2. **From Statement 2**: "In December 2016 he earned 10% more profit than in November 2016."
- This means:
\[
Z = Y + 0.1Y = 1.1Y
\]
3. **From Statement 3**: "The total profit earned in November 2016 and October 2016 was ₹55,000."
- This means:
\[
X + Y = 55,000
\]
### Step 3: Set Up Equations
From the first two statements, we have two equations:
1. \( Z = 1.4X \)
2. \( Z = 1.1Y \)
Since both equations equal \( Z \), we can set them equal to each other:
\[
1.4X = 1.1Y
\]
### Step 4: Solve for One Variable
From the equation \( 1.4X = 1.1Y \), we can express \( Y \) in terms of \( X \):
\[
Y = \frac{1.4X}{1.1} = \frac{14X}{11}
\]
### Step 5: Substitute into the Total Profit Equation
Now substitute \( Y \) in the total profit equation:
\[
X + \frac{14X}{11} = 55,000
\]
To combine the terms, we can find a common denominator:
\[
\frac{11X + 14X}{11} = 55,000
\]
\[
\frac{25X}{11} = 55,000
\]
### Step 6: Solve for \( X \)
Multiply both sides by 11:
\[
25X = 55,000 \times 11
\]
\[
25X = 605,000
\]
\[
X = \frac{605,000}{25} = 24,200
\]
### Step 7: Find \( Y \)
Now substitute \( X \) back to find \( Y \):
\[
Y = 55,000 - X = 55,000 - 24,200 = 30,800
\]
### Step 8: Find \( Z \)
Now, use either equation for \( Z \):
\[
Z = 1.4X = 1.4 \times 24,200 = 33,880
\]
### Conclusion
The profit earned by the shopkeeper in November 2016 is **₹30,800**.
