$N$ number of persons decided to raise ₹ 3 lakhs by equal contributions from each. Had they contributed ₹ 50 each extra, the contribution would have been ₹ 3.25 lakhs. How many persons are there?

### Concept & Logic This problem is based on basic algebraic formulation. The total contribution is the product of the number of persons and the contribution per person. We can set up a relationship based on the difference in the total amount collected. ### Step-by-Step Solution * **Given:** Initial total target is ₹ 3,00,000. If each person contributes ₹ 50 extra, the new total becomes ₹ 3,25,000. * **Calculation:** Let the initial contribution per person be $C$. * From the initial condition: $$N \times C = 300000$$ * From the changed condition: $$N \times (C + 50) = 325000$$ * Expand the second equation: $$N \times C + 50N = 325000$$ * Substitute the value of $N \times C$ from the first equation: $$300000 + 50N = 325000$$ $$50N = 25000$$ $$N = 500$$ ### Exam Strategy & Shortcut Instead of writing full equations, look at the net difference. The extra total amount collected is ₹ 3,25,000 - ₹ 3,00,000 = ₹ 25,000. This extra amount comes purely from every person giving ₹ 50 extra. Therefore, the number of persons must be $25000 / 50 = 500$. Since 500 is not in the options, select "None of these". ### Common Pitfall Students often waste time trying to find the individual contribution $C$ instead of isolating $N$, or they might guess "Cannot be determined" simply because 500 is missing from the explicit numerical choices. ### Final Answer **Therefore, the correct answer is None of these.**