A wholeseller offers 10% discount on pens which have been marked 60% above the cost price. Sumit bought the pen for Rs 504. What was the cost price (in Rs) of the pens?

Options

A. 220
B. 300
C. 350
D. 280

Answer

To find the cost price of the pens, we can follow these steps:

### Step 1: Understand the Marked Price
The wholesaler marks the price of the pens 60% above the cost price.
Let's assume the cost price (CP) of the pen is Rs 100.
Thus, the marked price (MP) will be:
\[ \text{MP} = \text{CP} + 60\% \text{ of CP} = 100 + 60 = Rs 160 \]

**Hint:** The marked price is calculated by adding the percentage increase to the original cost price.

### Step 2: Calculate the Selling Price after Discount
The wholesaler offers a 10% discount on the marked price.
To find the selling price (SP), we calculate:
\[ \text{Discount} = 10\% \text{ of MP} = 10\% \text{ of } 160 = 16 \]
So, the selling price will be:
\[ \text{SP} = \text{MP} - \text{Discount} = 160 - 16 = Rs 144 \]

**Hint:** The selling price can be found by subtracting the discount from the marked price.

### Step 3: Relate Selling Price to Actual Purchase
Sumit bought the pen for Rs 504.
From our calculations, we know that Rs 144 corresponds to the assumed cost price of Rs 100.
Now, we can set up a proportion to find the actual cost price:
\[ \frac{144}{100} = \frac{504}{\text{Cost Price}} \]

**Hint:** Use proportions to relate the selling price to the cost price.

### Step 4: Solve for the Cost Price
Cross-multiplying gives us:
\[ 144 \times \text{Cost Price} = 504 \times 100 \]
\[ \text{Cost Price} = \frac{50400}{144} \]

Now, we can simplify:
\[ \text{Cost Price} = \frac{50400}{144} = 350 \]

**Hint:** To find the cost price, divide the total amount paid by the ratio of selling price to cost price.

### Conclusion
Thus, the cost price of the pens is Rs 350.

### Final Answer
The cost price of the pens is Rs 350.

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