A man buys two chairs for a total cost of Rs. 900. By selling one for $$\frac{4}{5}$$ of its cost and the other for $$\frac{5}{4}$$ 
of its cost, he makes a profit of Rs. 90 on the whole transaction. The cost of the lower priced chair is

man buys two chairs for a total cost of Rs. 900

assume cost of lower priced chair = x

cost price of other chair = 900 - x

selling price of lower priced chair = $$ \frac{4}{5} x $$

selling price of other chair = $$ \frac{5}{4} \times (900 - x) $$

total CP = 900

total SP = $$ \frac{4}{5} x $$ + $$ \frac{5}{4} \times (900 - x) $$

SP - CP = PROFIT

$$ \frac{4}{5} x + \frac{5}{4}(900 - x) - 900 = 90 $$

$$ \frac{16x + 25(900 - x)}{20} = 990 $$

$$ 16x + 22500 - 25x = 990 \times 20 $$

solving x = 300