An item was bought at Rs. X and sold at Rs. Y, there by earning a profit of 20%. Had the value of X been 15% less and the value of Y been Rs. 76 less, a profit of 30% would have been earned. What was the value of ‘X’

C.P. = $$Rs. x$$

S.P. = $$Rs. y$$

Profit % = $$\frac{y - x}{x} \times 100 = 20$$

=> $$\frac{y - x}{x} = \frac{20}{100} = \frac{1}{5}$$

=> $$5y - 5x = x$$ => $$6x = 5y$$

=> $$y = \frac{6 x}{5}$$ -----------(i)

If, value of X been 15% less and the value of Y been Rs. 76 less

=> $$x' = \frac{85}{100} \times x = \frac{17 x}{20}$$

=> $$y' = y - 76$$

Profit % = $$\frac{y' - x'}{x'} \times 100 = 30$$

=> $$\frac{(y - 76) - (\frac{17 x}{20})}{\frac{17 x}{20}} = \frac{30}{100} = \frac{3}{10}$$

=> $$10 \times [(y - 76) - (\frac{17 x}{20}] = 3 \times \frac{17 x}{20}$$

=> $$10y - 760 - \frac{170 x}{20} = \frac{51 x}{20}$$

=> $$10y - \frac{221 x}{20} = 760$$

Using, equaiton (i), we get :

=> $$(10 \times \frac{6 x}{5}) - \frac{221 x}{20} = 760$$

=> $$12x - \frac{221 x}{20} = 760$$

=> $$\frac{19 x}{20} = 760$$

=> $$x = 760 \times \frac{20}{19}$$

=> $$x = 40 \times 20 = Rs. 800$$