Question

rs.6500 were divided equally among a certain number of persons. had there been 15 more persons, each would have got rs.30 less. find the original number of persons.

Answer 1

The original number of persons was found to be 65 by setting up an equation and solving a quadratic equation, taking into account that each person would get Rs.30 less if there were 15 more people.

Step-by-step explanation:

To find the original number of persons, we can set up an equation based on the information given. Let x be the original number of persons. Then each person would get Rs.6500/x when the money is divided equally. If there were 15 more persons, the number of persons would become x + 15, and each person would receive Rs.6500/(x + 15). We are told that in this case, each person would get Rs.30 less, so:

Rs.6500/x - Rs.30 = Rs.6500/(x + 15)

Now, we can solve for x:

1. Multiply both sides by x(x + 15) to eliminate the fractions: x(x + 15)(6500/x) - x(x + 15) * 30 = x(x + 15)(6500/(x + 15))
2. Simplify the equation: 6500(x + 15) - 30x(x + 15) = 6500x
3. Distribute and combine like terms: 6500x + 97500 - 30x^2 - 450x = 6500x
4. Subtract 6500x from both sides and simplify: -30x^2 - 450x + 97500 = 0
5. Divide by -30 to simplify the equation: x^2 + 15x - 3250 = 0
6. Factor the quadratic equation: (x + 50)(x - 65) = 0
7. Since the number of people cannot be negative, we take x = 65 as the solution.

Therefore, the original number of persons is 65.