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.

• A. $50$
• B. $55$
• C. $40$
• D. $65$

Answer 1

Answer: (A)

Total rupees$=Rs.6500$

Let original no. of persons$=x$

Money given to each person$=\frac{6500}{x}$

Now 15 more persons come, so total no. of people became$=x+15$.

Division of money among $x+15$ people$=\frac{6500}{x+15}$

But according to question, division of money among $(x+15)$ people=$\frac{6500}{x}-30$

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

$\Rightarrow 6500x=500x+6500\left(15\right)-30x(x+15)$

$\Rightarrow 30x^2+450x-6500\left(15\right)=0$

$\Rightarrow x^2+15x-3250=0$

$\Rightarrow x=\frac{-15\pm \sqrt{225+4\left(3250\right)}}{2}$

$\Rightarrow x=\frac{-15\pm 115}{2}$

$\Rightarrow x\ne -65$

$\Rightarrow x=50$

Hence option ${}^{\prime }{B}^{\prime }$ is the answer.