A shopkeeper sells a watch for Rs 960 after giving discount of 20% . Had he not given any discount he would earn 40% profit. At what price he sould sell that watch in order to earn profit of 54% .

Answer

To solve the problem step by step, we will first determine the cost price of the watch and then calculate the selling price required to achieve a 54% profit.

### Step 1: Determine the Marked Price (MP)
The shopkeeper sells the watch for Rs. 960 after giving a discount of 20%.

Let the marked price be \( MP \). The selling price (SP) after a discount can be expressed as:
\[ SP = MP - \text{Discount} \]
The discount is 20% of the marked price:
\[ \text{Discount} = 0.20 \times MP \]
So, we can rewrite the selling price as:
\[ SP = MP - 0.20 \times MP = 0.80 \times MP \]
Given that \( SP = 960 \):
\[ 0.80 \times MP = 960 \]
Now, we can solve for \( MP \):
\[ MP = \frac{960}{0.80} = 1200 \]

### Step 2: Determine the Cost Price (CP)
It is given that if the shopkeeper sells the watch at the marked price (Rs. 1200), he earns a profit of 40%.

The selling price (SP) is related to the cost price (CP) by the formula:
\[ SP = CP + \text{Profit} \]
Since the profit is 40% of the cost price, we can express it as:
\[ \text{Profit} = 0.40 \times CP \]
Thus, we have:
\[ SP = CP + 0.40 \times CP = 1.40 \times CP \]
Setting \( SP = 1200 \):
\[ 1.40 \times CP = 1200 \]
Now, we can solve for \( CP \):
\[ CP = \frac{1200}{1.40} = \frac{1200 \times 100}{140} = \frac{120000}{140} = 857.14 \text{ (approximately)} \]

### Step 3: Calculate Selling Price for 54% Profit
To find the selling price for a 54% profit, we will use the cost price we calculated:
\[ \text{Selling Price at 54% profit} = CP + \text{Profit} \]
The profit for 54% is:
\[ \text{Profit} = 0.54 \times CP \]
Thus, the selling price becomes:
\[ SP = CP + 0.54 \times CP = 1.54 \times CP \]
Substituting the value of \( CP \):
\[ SP = 1.54 \times 857.14 \approx 1320 \]

### Final Answer
The selling price at which the shopkeeper should sell the watch to earn a profit of 54% is **Rs. 1320**.

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