1)Rs,6500 were divided equally among a certain number of persons.if there had been 15 more person,each would have got Rs.30 less,find the original number of persons?
write it out into an equation: $\displaystyle \frac{6500}{p}=n$Originally Posted by anjana
now write out the second equation: $\displaystyle \frac{6500}{p+15}=n-30\quad\Rightarrow\quad\frac{6500}{p+15}+30=n$
therefore: $\displaystyle \frac{6500}{p}=\frac{6500}{p+15}+30$
Multiply both sides by "p+15" $\displaystyle \frac{6500p+97500}{p}=6500+30p+450$
multiply both sides by p: $\displaystyle 6500p+97500=6500p+30p^2+450p$
move everything to one side: $\displaystyle -30p^2+6500p-6500p-450p+97500=0$
subtract: $\displaystyle -30p^2-450p+97500=0$
and now you can use the quadratic formula (I hope you know how to do that)
I might as well continue:
using the quadratic formula you get: $\displaystyle p=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
substitute: $\displaystyle p=\frac{-(-450)\pm\sqrt{(-450)^2-4(-30)(97500)}}{2(-30)}$
multiply: $\displaystyle p=\frac{450\pm\sqrt{202500+11700000}}{-60}$
add: $\displaystyle p=\frac{450\pm\sqrt{11902500}}{-60}$
find sqrt: $\displaystyle p=\frac{450\pm3450}{-60}$
split equation: $\displaystyle p=\left\{\begin{array}{cc}(450-3450)\div-60=-3000\div-60=50\\(450+3450)\div-60=3900\div-60=-65\end{array}\left$
therefore, after throwing away the negative answer, there were 50 people