Question

Rs.6500 is divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs.30 less. Find the number of persons.

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Original number of persons = p

Given,

Amount to be divided :-

= 6500

Each of share :-

= 6500/p

Another number of persons :-

= p + 15

Share of each another :-

= 6500/p + 15

Situation,

6500/p - 6500/p + 15 = 30

1/p - 1/(p + 15) = 30/6500

(p + 15) - p/p(p + 15) = 3/650

15/(p² + 15p) = 3/650

3(p² + 15) = 9750

p² + 15p = 3250

p² + 15p - 3250 = 0

p² + 65p - 50p - 3250 = 0

p(p + 65) - 50(p + 50) = 0

(p + 65)(p + 50) = 0

p + 65 = 0 or p - 50 = 0

p = - 65, 50 (Negative value is not applicable)

So,

p = 50

Therefore,

Original number of persons = 50