An oil merchant wants to make a minimum profit of Rs 2, 100 by selling 50 litres of oil he purchased at Rs 236 per litre. For this, be adds a few litres of duplicate oil whose cosi price is Rs 180 per liire and sells at Rs 250 per litre. How many litres of duplicate oil is needed for this purpose?

Options

A. 18 litres
B. 22 litres
C. 20 litres
D. 16 litres

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the total cost of the original oil
The oil merchant purchased 50 litres of oil at Rs 236 per litre.
\[ \text{Total cost of original oil} = 50 \text{ litres} \times 236 \text{ Rs/litre} = 11800 \text{ Rs} \]

**Hint:** Multiply the quantity of oil by its cost price to find the total cost.

### Step 2: Set up the equation for profit
The merchant wants to make a minimum profit of Rs 2100. Therefore, the total revenue from selling all the oil (original + duplicate) must be:
\[ \text{Total Revenue} = \text{Total Cost} + \text{Profit} \]
\[ \text{Total Revenue} = 11800 \text{ Rs} + 2100 \text{ Rs} = 13900 \text{ Rs} \]

**Hint:** Add the desired profit to the total cost to find the required total revenue.

### Step 3: Determine the selling price of the oil
The selling price of the oil (both original and duplicate) is Rs 250 per litre. Let \( x \) be the number of litres of duplicate oil added. Therefore, the total quantity of oil sold is \( 50 + x \) litres.
\[ \text{Total Revenue} = (50 + x) \text{ litres} \times 250 \text{ Rs/litre} \]
Setting this equal to the total revenue calculated in Step 2:
\[ (50 + x) \times 250 = 13900 \]

**Hint:** Use the selling price to express total revenue in terms of quantity.

### Step 4: Expand and simplify the equation
Expanding the equation:
\[ 12500 + 250x = 13900 \]
Now, subtract 12500 from both sides:
\[ 250x = 13900 - 12500 \]
\[ 250x = 1400 \]

**Hint:** Rearrange the equation to isolate the variable.

### Step 5: Solve for \( x \)
Now, divide both sides by 250 to find \( x \):
\[ x = \frac{1400}{250} = 5.6 \]

**Hint:** Divide to find the quantity of duplicate oil required.

### Step 6: Conclusion
Since \( x \) must be a whole number (you cannot add a fraction of a litre), round \( x \) up to the nearest whole number. Thus, the merchant needs to add 6 litres of duplicate oil to achieve the desired profit.

**Final Answer:** The merchant needs to add **6 litres** of duplicate oil.