Jayashree purchased 150 kg of wheat of the rate of 7 per kg. She sold 50 kg at a profit of 10%. At what rate per kg should she sell the remaining to get a profit of 20% on the total deal?
A)6.5
B)8.75
C)7.5
D)9.75

Options

A. 6.5
B. 8.75
C. 7.5
D. 9.75

Answer

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

### Step 1: Calculate the Total Cost Price (CP) of Wheat
Jayashree purchased 150 kg of wheat at the rate of 7 per kg.

\[ \text{Total Cost Price} = \text{Quantity} \times \text{Rate per kg} = 150 \, \text{kg} \times 7 \, \text{per kg} = 1050 \]

### Step 2: Calculate the Selling Price (SP) of the First 50 kg Sold
Jayashree sold 50 kg of wheat at a profit of 10%.

First, we calculate the cost price of the 50 kg:

\[ \text{Cost Price of 50 kg} = 50 \, \text{kg} \times 7 \, \text{per kg} = 350 \]

Now, calculate the selling price with a 10% profit:

\[ \text{Profit} = 10\% \text{ of } 350 = \frac{10}{100} \times 350 = 35 \]

\[ \text{Selling Price of 50 kg} = \text{Cost Price} + \text{Profit} = 350 + 35 = 385 \]

### Step 3: Calculate the Total Selling Price Needed for 20% Profit
To find out how much total selling price is needed for a 20% profit on the total cost price:

\[ \text{Required Total Selling Price} = \text{Total Cost Price} + \text{20% of Total Cost Price} \]

\[ \text{20% of Total Cost Price} = \frac{20}{100} \times 1050 = 210 \]

\[ \text{Required Total Selling Price} = 1050 + 210 = 1260 \]

### Step 4: Calculate the Selling Price of the Remaining Wheat
Jayashree sold 50 kg for 385, so the selling price of the remaining 100 kg must be:

\[ \text{Selling Price of Remaining 100 kg} = \text{Required Total Selling Price} - \text{Selling Price of 50 kg} \]

\[ \text{Selling Price of Remaining 100 kg} = 1260 - 385 = 875 \]

### Step 5: Calculate the Rate per kg for the Remaining Wheat
Now, we need to find the rate per kg for the remaining 100 kg of wheat:

\[ \text{Rate per kg} = \frac{\text{Selling Price of Remaining 100 kg}}{\text{Quantity}} = \frac{875}{100} = 8.75 \]

### Final Answer
Jayashree should sell the remaining wheat at a rate of **8.75 per kg** to achieve a total profit of 20%.

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