A person had 100 kg sugar. He sold some part at 7% profit and rest at a profit of 17%. By doing so he gains a profit of 10% on whole transaction. How much sugar did he sell at 7% profit ?
एक व्यक्ति के पास 100 कि.ग्रा. चीनी थी जिसका कुछ भाग उसने 7% लाभ पर तथा बाकी 17% लाभ पर बेचा। ऐसा करने से उसे सम्पूर्ण पर 10% लाभ हुआ। 7% लाभ पर उसने कितनी चीनी बेची?

Options

A. 65 कि. ग्रा.
B. 35 कि. ग्रा०
C. 30 कि. ग्रा.
D. 70 कि. ग्रा.

Explanation

To solve the problem step by step, we will use the allegation method as described in the video transcript.

### Step 1: Understand the given data
- Total sugar = 100 kg
- Profit on part sold at 7% = 7%
- Profit on part sold at 17% = 17%
- Overall profit = 10%

### Step 2: Set up the allegation
Using the allegation method, we will find the ratio in which the sugar is sold at different profits.

1. Write down the profits:
- Profit at lower rate (7%) = 7%
- Profit at higher rate (17%) = 17%
- Overall profit (10%) = 10%

2. Set up the allegation:
- The difference between 10% and 7% is \(10 - 7 = 3\)
- The difference between 17% and 10% is \(17 - 10 = 7\)

### Step 3: Determine the ratio
From the differences calculated:
- The ratio of sugar sold at 7% profit to sugar sold at 17% profit is \(7:3\).

### Step 4: Calculate the amount of sugar sold at each profit
Let the amount of sugar sold at 7% profit be \(7x\) and the amount sold at 17% profit be \(3x\).

Since the total amount of sugar is 100 kg:
\[ 7x + 3x = 100 \]
\[ 10x = 100 \]
\[ x = 10 \]

### Step 5: Calculate the quantities
Now, substituting \(x\) back to find the quantities:
- Amount sold at 7% profit = \(7x = 7 \times 10 = 70\) kg
- Amount sold at 17% profit = \(3x = 3 \times 10 = 30\) kg

### Final Answer
The amount of sugar sold at 7% profit is **70 kg**.

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