King Dashratha of Ayodhya on his birthday decided to offer 100 coins of gold among his 4 sons and 3 wives. The denomination of each coin is `₹`1. He put all the 100 coins in 7 bags in such a way that by taking a proper combination of various bags any integral sum (i.e. `₹` 1, 2, 3, 4, ... .100) can be obtained and it is known that the only whole sum of any bag can be taken.
If all coins, of these who have odd number of coins, are combined then minimum how many people are required to combine their coins to make the same amount having even number of coins:

Options

A. 2
B. 3
C. 4
D. can't be determined

Answer

To solve the problem, we need to determine how many people with an odd number of coins can combine their coins to make an even number of coins. Let's break down the solution step by step:

### Step 1: Understand the Distribution of Coins
King Dashratha has 100 coins to distribute among 7 people (4 sons and 3 wives).

### Step 2: Calculate Average Distribution
If we divide 100 coins among 7 people, we get:
\[ \text{Average coins per person} = \frac{100}{7} \approx 14.2857 \]
Since we cannot distribute fractional coins, we need to round down.

### Step 3: Determine Whole Number Distribution
If each person receives 14 coins, then:
\[ \text{Total coins distributed} = 14 \times 7 = 98 \]
This leaves us with:
\[ 100 - 98 = 2 \text{ coins remaining} \]

### Step 4: Assign Remaining Coins
To distribute the remaining 2 coins, we can give them to any 2 of the 7 people. This means that these 2 people will have:
\[ 14 + 1 = 15 \text{ coins each} \]
Thus, we have:
- 5 people with 14 coins (even)
- 2 people with 15 coins (odd)

### Step 5: Identify Odd and Even Coin Holders
From the distribution:
- Odd holders: 2 people (each with 15 coins)
- Even holders: 5 people (each with 14 coins)

### Step 6: Combining Odd Coin Holders to Make Even
To make an even number from odd holders, we can combine the coins of the odd holders. The sum of two odd numbers is always even. Therefore, the minimum number of odd holders required to make an even sum is:
\[ \text{Minimum odd holders required} = 2 \]

### Final Answer
Thus, the minimum number of people required to combine their coins to make the same amount having an even number of coins is:
\[ \boxed{2} \]