In the price of sugar falls by $$2\frac{1}{2}\% $$ , a person can buy 9 kg more of sugar for Rs. 1260 than before. If the price had risen by $$12\frac{1}{2}\% $$ , how much sugar would he have bought for the same sum ?

Solution(By Examveda Team)

Let the original price of sugar be Rs. $$x$$ per kg
Then, reduced price :
$$\eqalign{ & 97\frac{1}{2}\% {\text{ of Rs}}{\text{. }}x \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{195}}{2} \times \frac{1}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{39x}}{{40}} \cr & \therefore \frac{{1260}}{{\left( {\frac{{39x}}{{40}}} \right)}} - \frac{{1260}}{x} = 9 \cr & \Rightarrow \frac{{16800}}{{13x}} - \frac{{1260}}{x} = 9 \cr & \Rightarrow 13x = \frac{{420}}{9} \cr & \Rightarrow x = \frac{{140}}{{39}} \cr} $$
Increased price :
$$\eqalign{ & 112\frac{1}{2}\% {\text{ of Rs}}{\text{. }}\frac{{140}}{{39}} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{225}}{2} \times \frac{1}{{100}} \times \frac{{140}}{{39}}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{105}}{{26}} \cr} $$
∴ Quiantity of sugar bought for Rs. 1260 :
$$\eqalign{ & = \left( {1260 \times \frac{{26}}{{105}}} \right){\text{ kg}} \cr & = {\text{312 kg}} \cr} $$