A shopkeeper placed a supply order for jeans, shirts and t-shirts at the rates of Rs. 500, Rs.350 and Rs.200 per piece, respectively. He buys articles of each type in the ratio 1:2:3 for Rs. 46,800. For how many t-shirts did he place the order?

Options

A. 104
B. 26
C. 78
D. 52

Answer

To solve the problem, we need to find out how many t-shirts the shopkeeper ordered based on the given information.

### Step 1: Define Variables
Let:
- The number of jeans ordered = \( x \)
- The number of shirts ordered = \( 2x \) (since the ratio is 1:2:3)
- The number of t-shirts ordered = \( 3x \)

### Step 2: Calculate the Total Cost
The cost of each type of clothing is given as follows:
- Cost of jeans = Rs. 500 per piece
- Cost of shirts = Rs. 350 per piece
- Cost of t-shirts = Rs. 200 per piece

Now, we can express the total cost based on the quantities:
\[ \text{Total Cost} = (\text{Cost of jeans}) + (\text{Cost of shirts}) + (\text{Cost of t-shirts}) \]
\[ = 500x + 350(2x) + 200(3x) \]

### Step 3: Simplify the Total Cost Expression
Substituting the values:
\[ = 500x + 700x + 600x \]
\[ = (500 + 700 + 600)x = 1800x \]

### Step 4: Set Up the Equation
According to the problem, the total cost is Rs. 46,800. Therefore, we can set up the equation:
\[ 1800x = 46800 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 1800:
\[ x = \frac{46800}{1800} \]
\[ x = 26 \]

### Step 6: Calculate the Number of T-shirts
Since the number of t-shirts ordered is \( 3x \):
\[ \text{Number of t-shirts} = 3x = 3 \times 26 = 78 \]

### Final Answer
The shopkeeper placed an order for **78 t-shirts**.

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