By selling 90 chocolates for Rs. 160, a chocolate trader loss `20%` How many chocolates should he sell for Rs. 96 to make a profit of `20%`

Options

A. 45
B. 36
C. 54
D. 28

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Determine the Cost Price of One Chocolate
We know that selling 90 chocolates for Rs. 160 results in a loss of 20%.

Let the cost price (CP) of one chocolate be \( x \).

Since there is a 20% loss, the selling price (SP) can be calculated as:
\[ SP = CP - (20\% \text{ of } CP) = CP \times (1 - 0.20) = 0.80 \times CP \]

Given that the selling price for 90 chocolates is Rs. 160, we can write:
\[ 0.80 \times (90 \times x) = 160 \]
\[ 72x = 160 \]
\[ x = \frac{160}{72} = \frac{20}{9} \]

### Step 2: Calculate the Selling Price for Profit
Now, we need to find out how many chocolates should be sold for Rs. 96 to make a profit of 20%.

If we want to make a profit of 20%, the selling price (SP) should be:
\[ SP = CP + (20\% \text{ of } CP) = CP \times (1 + 0.20) = 1.20 \times CP \]

Substituting the cost price we found:
\[ SP = 1.20 \times \frac{20}{9} = \frac{24}{9} = \frac{8}{3} \]

### Step 3: Determine the Number of Chocolates to Sell for Rs. 96
Now, we need to determine how many chocolates (let's denote this number as \( n \)) can be sold for Rs. 96 at the selling price of \( \frac{8}{3} \) per chocolate.

The total selling price for \( n \) chocolates will be:
\[ n \times \frac{8}{3} = 96 \]
To find \( n \):
\[ n = \frac{96 \times 3}{8} = \frac{288}{8} = 36 \]

### Conclusion
Thus, the chocolate trader should sell **36 chocolates** for Rs. 96 to make a profit of 20%.

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