A college 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 represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what would be the average donation from the remaining people to be solicited?

Given:

The college has raised 75% of the total amount needed by receiving an average donation of ₹600 from 60% of the people who will be solicited.

Let the total number of people to be solicited be P, and the total amount required be A.

Formula used:

The amount raised so far = 75% of A = 0.75A.

The number of people already solicited = 60% of P = 0.60P.

The average donation from these people = ₹600.

Therefore, the total amount raised so far is:

Total amount raised so far = 0.60P × 600 = 0.75A.

Calculation:

⇒ 0.60P × 600 = 0.75A

⇒ 360P = 0.75A

⇒ A = (360P ÷ 0.75) = 480P

Now, the amount needed from the remaining 40% of people = A - 0.75A = 0.25A = 0.25 × 480P = 120P.

The remaining 40% of people = 0.40P.

The average donation required from the remaining people = (Amount to be raised) ÷ (Remaining people) = 120P ÷ 0.40P = ₹300.

∴ The average donation from the remaining people must be ₹300.