Ram sells only two kinds of bags , pure leather and faux leather. `75%` and `80%` of the total number of bags sold, in February and March respectively, were of pure leather. Average number of pure leather bags sold in both the months is 5850 and the total number of bags sold in March is `50%` more than that sold in February. How many faux leather bags did Ram sell in February?

Options

A. 2000
B. 1600
C. 1500
D. 1800

Answer

To solve the problem step by step, let's break down the information provided and calculate the number of faux leather bags sold by Ram in February.

### Step 1: Define Variables
Let:
- Total bags sold in February = \( F \)
- Total bags sold in March = \( M \)

### Step 2: Establish Relationships
According to the problem:
- \( M = F + 0.5F = 1.5F \) (March sales are 50% more than February sales)
- Average number of pure leather bags sold in both months = 5850

### Step 3: Calculate Pure Leather Bags Sold
From the problem:
- 75% of bags sold in February are pure leather: \( 0.75F \)
- 80% of bags sold in March are pure leather: \( 0.8M \)

### Step 4: Substitute March Sales in Terms of February
Substituting \( M \) in the equation for pure leather bags sold in March:
\[ 0.8M = 0.8(1.5F) = 1.2F \]

### Step 5: Total Pure Leather Bags Sold
Now, we can find the total number of pure leather bags sold in both months:
\[ \text{Total pure leather bags} = 0.75F + 1.2F = 1.95F \]

### Step 6: Average Calculation
The average number of pure leather bags sold in both months is given as 5850, which means:
\[ \frac{1.95F}{2} = 5850 \]

### Step 7: Solve for F
To find \( F \):
\[ 1.95F = 5850 \times 2 \]
\[ 1.95F = 11700 \]
\[ F = \frac{11700}{1.95} \]
\[ F = 6000 \]

### Step 8: Calculate Total Bags Sold in March
Now that we have \( F \):
\[ M = 1.5F = 1.5 \times 6000 = 9000 \]

### Step 9: Calculate Faux Leather Bags Sold in February
Faux leather bags sold in February are 25% of the total bags sold in February:
\[ \text{Faux leather bags in February} = 0.25F = 0.25 \times 6000 = 1500 \]

### Final Answer
Ram sold **1500 faux leather bags in February.**

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