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Rs.$6500$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $Rs.30$ less. Find the original number of persons.

  1. $50$
  2. $60$
  3. $45$
  4. $55$
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Answer is A

Let the number of persons be x

$\frac{6500}{x}=\frac{6500}{x+15}+30$

$\frac{6500}{x}-\frac{6500}{x+15}=30$

$6500 *(\frac{1}{x}-\frac{1}{x+15})=30$$6500 *\frac{x+15-x}{x(x+15)}=30$

$x^{2}+15x-3250=0$ 

Roots of the equation $ax^2 + bx +c = 0$ are given by $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.$ 

So, we get $ x = \dfrac{-15 \pm \sqrt{225 +13000}}{2} = \dfrac{-15 \pm 115}{2} =50, -65$

Number of persons cannot be negative. So, x = 50

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