A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for Rs. 100. What is the reduced price per kg ?

Answer: Option A

Let the original price = Rs. $$x$$ per kg
Reduced price = Rs. $$\left(\frac{79x}{100}\right)$$ per kg
$$\begin{array}{rl}& \therefore \frac{100}{79x}-\frac{100}{x}=10.5\\ & \Rightarrow \frac{10000}{79x}-\frac{100}{x}=10.5\\ & \Rightarrow 10000-7900=10.5\times 79x\\ & \Rightarrow x=\frac{2100}{10.5\times 79}\end{array}$$
∴ Reduced price :
$$\begin{array}{rl}& =\text{Rs}\text{. }\left(\frac{79}{100}\times \frac{2100}{10.5\times 79}\right)\text{ per kg}\\ & =\text{Rs}\text{. 2 per kg}\end{array}$$