Mewalal is selling fruits in charbagh, Lucknow, which were imported from Kesharbagh and Dayalbagh only. He has 13 apples, 25 bananas, 17 cherries, 29 goose berries, 35 mangoes and 42 pine apples. When I wanted to purchase some fruits from his shop, he told me that he can sell only in lots(i.e.,either total apples or total bananas or 10 apples) and he told me that he himself can import any type of fruits without any lot, sya 20 mangoes from Kesharbagh and 15 mangoes from Dayalbagh and so on if he wished.
As per the given constraints if Mewalal has sold some fruits in such a way that he is now left with 3/4 fruits of Dayalbagh than that of Kesarbagh. Maximum how many lots (i.e., categories) of fruits he can sell out in such a way?

Options

A. 1
B. 2
C. 3
D. can't be determined

Answer

To solve the problem step by step, we will first calculate the total number of fruits Mewalal has, then determine how many fruits he has left after selling some, and finally analyze how many lots of fruits he can sell.

### Step 1: Calculate the Total Number of Fruits
Mewalal has the following fruits:
- Apples: 13
- Bananas: 25
- Cherries: 17
- Gooseberries: 29
- Mangoes: 35
- Pineapples: 42

**Total Fruits = Apples + Bananas + Cherries + Gooseberries + Mangoes + Pineapples**

Total Fruits = 13 + 25 + 17 + 29 + 35 + 42

Total Fruits = 161

### Step 2: Determine the Number of Fruits Left
According to the problem, Mewalal is left with \( \frac{3}{4} \) of the fruits from Dayalbagh compared to Kesharbagh.

Let’s denote:
- Total fruits left = \( \frac{3}{4} \) of Dayalbagh fruits
- Let \( D \) be the number of fruits from Dayalbagh and \( K \) be the number of fruits from Kesharbagh.

From the problem, we know that:
\[ \text{Fruits Left} = \frac{3}{4}D \]

Since the total number of fruits is 161, we can find the number of fruits sold:
\[ \text{Fruits Sold} = \text{Total Fruits} - \text{Fruits Left} \]

### Step 3: Calculate Fruits Left
If Mewalal has sold some fruits and is left with \( \frac{3}{4}D \), we need to find out how many fruits he has left.

Let’s denote the total fruits left as \( L \):
\[ L = \frac{3}{4}D \]

We can express the total fruits left in terms of the total fruits:
\[ L = 161 - \text{Fruits Sold} \]

### Step 4: Calculate Fruits Sold
From the above, we can express the number of fruits sold:
\[ \text{Fruits Sold} = 161 - L \]

### Step 5: Determine the Maximum Number of Lots
Mewalal can sell fruits in lots of either the total number of a specific fruit or in lots of 10 apples. We need to consider the types of fruits he has:
- Apples: 13
- Bananas: 25
- Cherries: 17
- Gooseberries: 29
- Mangoes: 35
- Pineapples: 42

Since he can sell only whole lots, we can determine the maximum lots he can sell based on the total number of each fruit type.

### Conclusion
To find the maximum number of lots he can sell:
- He can sell all of each type of fruit (1 lot each for apples, bananas, cherries, gooseberries, mangoes, and pineapples).
- He can also sell 10 apples as a separate lot.

Thus, the maximum number of lots he can sell is:
- 1 lot of apples
- 1 lot of bananas
- 1 lot of cherries
- 1 lot of gooseberries
- 1 lot of mangoes
- 1 lot of pineapples
- 1 additional lot of 10 apples (if he chooses to sell them in this way)

This gives us a total of 7 lots.

### Final Answer
Mewalal can sell a maximum of **7 lots** of fruits.

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