A club has raised `75%` of the amount it needs for a new building by receiving an average donation of ₹ 600 from the people already solicited. The people already solicited represents `60%` of the people the club will ask for donations. If the club is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?

Options

A. 250
B. 300
C. 400
D. 600

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Calculate the total amount needed for the new building.
We know that the club has raised 75% of the total amount needed. Let’s denote the total amount needed as \( x \).

Given that 75% of \( x \) is the amount already raised, we can express this mathematically:
\[ \text{Amount raised} = 0.75x \]

### Step 2: Calculate the amount already raised.
The average donation from the people already solicited is ₹600, and they represent 60% of the total people to be asked for donations. Let’s denote the total number of people to be solicited as \( P \).

The number of people already solicited is:
\[ 0.6P \]

Thus, the total amount raised from these people is:
\[ \text{Amount raised} = \text{Number of people} \times \text{Average donation} = 0.6P \times 600 \]
This can be simplified to:
\[ \text{Amount raised} = 360P \]

### Step 3: Set the two expressions for the amount raised equal to each other.
From Step 1 and Step 2, we have:
\[ 0.75x = 360P \]

### Step 4: Calculate the total amount needed for the building.
To find \( x \), we can rearrange the equation:
\[ x = \frac{360P}{0.75} = 480P \]

### Step 5: Calculate the remaining amount needed.
The amount already raised is \( 0.75x \), so the remaining amount needed is:
\[ \text{Remaining amount} = x - 0.75x = 0.25x \]
Substituting \( x \) from Step 4:
\[ \text{Remaining amount} = 0.25 \times 480P = 120P \]

### Step 6: Calculate the number of remaining people to be solicited.
Since 60% of the people have already been solicited, the remaining percentage is:
\[ 100\% - 60\% = 40\% \]
Thus, the number of remaining people is:
\[ \text{Remaining people} = 0.4P \]

### Step 7: Calculate the average donation required from the remaining people.
To find the average donation needed from the remaining people, we divide the remaining amount by the number of remaining people:
\[ \text{Average donation} = \frac{\text{Remaining amount}}{\text{Remaining people}} = \frac{120P}{0.4P} \]
This simplifies to:
\[ \text{Average donation} = \frac{120}{0.4} = 300 \]

### Final Answer:
The average donation required from the remaining people to be solicited is ₹300.

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