If the price of sugar falls by $2 \frac{1}{2} \%$, a person can buy 9 kg more of sugar for ₹ 1260 than before. If the price had risen by $12 \frac{1}{2} \%$, how much sugar would he have bought for the same sum?
(a)288 kg
(b)312 kg
(c)328 kg
(d)336 kg
Answer
Answer (as printed): B
Explanation
Let the original price of sugar be ₹ $x$ per kg. Then, reduced price $=97 \frac{1}{2} \%$ of $₹ x$ $$=₹\left(\frac{195}{2} \times \frac{1}{100} \times x\right)=₹ \frac{39 x}{40} .$$ $\therefore \frac{1260}{\left(\frac{39 x}{40}\right)}-\frac{1260}{x}=9 \Rightarrow \frac{16800}{13 x}-\frac{1260}{x}=9$ $$\Leftrightarrow 13 x=\frac{420}{9} \Rightarrow x=\frac{140}{39} .$$ Increased price = $112 \frac{1}{2} \%$ of ₹ $\frac{140}{39}$ $$=₹\left(\frac{225}{2} \times \frac{1}{100} \times \frac{140}{39}\right)=₹ \frac{105}{26} .$$ ∴ Quantity of sugar bought for ₹ 1260 $$=\left(1260 \times \frac{26}{105}\right) \mathrm{kg}=312 \mathrm{kg} .$$