An article is sold at a certai fixed price. By selling it at $$\frac{2}{3}$$ of that price, one loses 10%. The gain per cent on selling it at the original price is
Cost price (CP), Selling price (SP), Loss (L)
let original SP = x
new SP = $$ \frac{2}{3}x $$
CP = $$ \frac{100}{100 - L} \times SP $$
given L =10%
CP = $$ \frac{100}{90} \times\frac{2x}{3} = \frac{20x}{27} $$
SP = X
Gain = x - $$ \frac{20x}{27} = \frac{7x}{27} $$
gain % = $$ \frac{\frac{7x}{27}}{\frac{20x}{27}} = \frac{7}{20} \times 100 = 35% $$
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