A man buys some quantity of wheat for 2400. He sells one third of it at a profit of 5%. At what per cent gain should he sell the remaining two-third so as to make an overall profit of 10% on the whole transaction?

Options

A. 0.115
B. 0.125
C. 0.13
D. 0.135

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the total cost and desired profit
The man buys wheat for ₹2400. He wants to achieve an overall profit of 10%.

**Hint:** Calculate the total selling price needed to achieve the desired profit.

Total Selling Price (SP) for 10% profit = Cost Price (CP) + Profit
\[ SP = 2400 + (10\% \text{ of } 2400) \]
\[ SP = 2400 + 240 = ₹2640 \]

### Step 2: Calculate the selling price of the first one-third of wheat
He sells one-third of the wheat at a profit of 5%.

**Hint:** Calculate the selling price for one-third of the wheat.

Cost of one-third of wheat = \( \frac{2400}{3} = ₹800 \)
Selling Price (SP) for one-third at 5% profit = Cost Price + Profit
\[ SP = 800 + (5\% \text{ of } 800) \]
\[ SP = 800 + 40 = ₹840 \]

### Step 3: Calculate the remaining selling price needed
Now, we need to find out how much more he needs to earn from the remaining two-thirds of the wheat to reach the total selling price of ₹2640.

**Hint:** Subtract the selling price of the first one-third from the total selling price.

Remaining Selling Price needed = Total Selling Price - Selling Price of one-third
\[ Remaining SP = 2640 - 840 = ₹1800 \]

### Step 4: Calculate the cost of the remaining two-thirds of wheat
The cost of the remaining two-thirds of the wheat is:

**Hint:** Calculate the cost for the remaining two-thirds.

Cost of two-thirds of wheat = \( \frac{2400 \times 2}{3} = ₹1600 \)

### Step 5: Determine the required profit percentage on the remaining two-thirds
To find the required profit percentage on the remaining two-thirds, we need to calculate the profit made on this portion.

**Hint:** Use the formula for profit percentage.

Profit = Selling Price - Cost Price
\[ Profit = 1800 - 1600 = ₹200 \]

Now, calculate the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{Profit}{Cost Price} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{200}{1600} \right) \times 100 = 12.5\% \]

### Final Answer
The man should sell the remaining two-thirds of the wheat at a gain of **12.5%** to achieve an overall profit of 10%.

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