A reduction of 20% in the price of salt enabled a purchaser to obtain 4 kg, more for Rs. 100. The reduced price of salt per kg. is = ?

Solution(By Examveda Team)

Let the original price of salt per kg. is Rs. x
So, purchaser can buy $$\frac{{100}}{x}$$ kg.
Now, reduction price is 20%
Salt per kg. $$ = x \times \frac{{80}}{{100}} = {\text{Rs}}{\text{.}}\,\frac{{4x}}{5}$$
Now purchaser can buy
$$\eqalign{ & \frac{{100}}{{\frac{{4x}}{5}}} = \frac{{125}}{x}\,{\text{kg}} \cr & \therefore \frac{{125}}{x} - \frac{{100}}{x} = 4\,{\text{kg}} \cr & \Rightarrow \frac{{25}}{x} = 4 \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,6.25 \cr} $$
Hence the reduced price of salt per kg.
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,6.25 \times \frac{{80}}{{100}} \cr & = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$

Alternate:
$$\eqalign{ & {\text{Trick}} = \frac{a}{x} \times \frac{{{\text{reduction}}}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{4} \times \frac{{20}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$