In the price of sugar falls by 21/2\% , a person can buy 9 kg more of sugar for Rs. 1260 than before. If the price had risen by 121/2\% , how much sugar would he have bought for the same sum ?

Answer: Option B

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