let number of people be X.

1^{st} equation = 6500/X

2^{nd} equation= 6500/ 15+X

asper question when 15 people werwe more then 30 rupees were less with everyone.

therefore, 6500/X- 6500/ X+15 = 30

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

6500(X+15- X / X^{2} + 15X) = 30

6500(15/X^{2}+ 15X)= 30

6500(15) = 30(X^{2} + 15X)

6500(15) = 30X^{2} +30(15X) [TAKING 15 COMMON]

6500 = 2X^{2} + 30X

0 = 2X^{2} +30X - 6500 [TAKING 2 COMMON]

0 = X^{2} +15X - 3250

0 = X^{2} +(65X - 50X) - 3250[MIDDLE TERM FACTORISATION]

0 = X^{2} +65X - 50X - 3250

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

THEREFORE , X = 50 PEOPLE.

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