A ready-made garments shop in Delhi allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shopkeeper for Rs 400.

Answer

To solve the problem, we need to find the marked price of a dress that the shopkeeper bought for Rs 400, given that the shop allows a 20% discount and still makes a profit of 20%.

Let's break this down step by step:

### Step 1: Calculate the Selling Price (SP)
The profit percentage is given as 20%. We can use the formula for profit percentage:

\[ \text{Profit Percentage} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100 \]

Given that the Cost Price (CP) is Rs 400, we can set up the equation:

\[ 20 = \frac{SP - 400}{400} \times 100 \]

### Step 2: Solve for Selling Price (SP)
Rearranging the equation to find SP:

\[ 20 = \frac{SP - 400}{400} \times 100 \]

Dividing both sides by 100:

\[ 0.2 = \frac{SP - 400}{400} \]

Multiplying both sides by 400:

\[ 80 = SP - 400 \]

Adding 400 to both sides:

\[ SP = 480 \]

### Step 3: Calculate the Marked Price (MP)
Now, we know the Selling Price (SP) is Rs 480. The shop allows a 20% discount on the marked price. We can use the discount formula:

\[ \text{Discount Percentage} = \frac{\text{Marked Price} - \text{Selling Price}}{\text{Marked Price}} \times 100 \]

Setting up the equation with a discount of 20%:

\[ 20 = \frac{MP - 480}{MP} \times 100 \]

### Step 4: Solve for Marked Price (MP)
Rearranging the equation to find MP:

\[ 20 = \frac{MP - 480}{MP} \times 100 \]

Dividing both sides by 100:

\[ 0.2 = \frac{MP - 480}{MP} \]

Multiplying both sides by MP:

\[ 0.2 \cdot MP = MP - 480 \]

Rearranging gives:

\[ MP - 0.2 \cdot MP = 480 \]

Combining like terms:

\[ 0.8 \cdot MP = 480 \]

Dividing both sides by 0.8:

\[ MP = \frac{480}{0.8} = 600 \]

### Conclusion
The marked price of the dress is Rs 600.

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