Maha Bazaar offers 20% discount on bags which have been marked 50% above the cost price. Amarnath pays Rs. 840 for bag. Then the cost price of the bag is

Options

A. Rs. 672
B. Rs. 700
C. Rs. 790
D. Rs. 810

Answer

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

### Step 1: Understand the relationship between cost price (CP), marked price (MP), and selling price (SP).
- Let's denote the cost price of the bag as CP.
- The marked price is 50% above the cost price, which means:
\[ \text{MP} = \text{CP} + 0.5 \times \text{CP} = 1.5 \times \text{CP} \]

### Step 2: Calculate the marked price.
- If we assume the cost price (CP) is 100 (for easier calculations), then:
\[ \text{MP} = 1.5 \times 100 = 150 \]

### Step 3: Calculate the selling price after the discount.
- Maha Bazaar offers a 20% discount on the marked price. Therefore, the discount amount is:
\[ \text{Discount} = 20\% \text{ of MP} = 0.2 \times 150 = 30 \]
- The selling price (SP) after the discount is:
\[ \text{SP} = \text{MP} - \text{Discount} = 150 - 30 = 120 \]

### Step 4: Set up the equation with the selling price.
- According to the problem, Amarnath pays Rs. 840 for the bag, which means:
\[ \text{SP} = 840 \]

### Step 5: Relate the selling price to the cost price.
- From our earlier calculation, we found that the selling price in terms of CP is:
\[ \text{SP} = 1.2 \times \text{CP} \]
- Setting this equal to the amount Amarnath paid:
\[ 1.2 \times \text{CP} = 840 \]

### Step 6: Solve for the cost price (CP).
- To find CP, we rearrange the equation:
\[ \text{CP} = \frac{840}{1.2} \]
- Calculating this gives:
\[ \text{CP} = 700 \]

### Conclusion:
- The cost price of the bag is Rs. 700.

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