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 R…

Solution
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 :
=> $(10 \times \frac{6 x}{5}) - \frac{221 x}{20} = 760$
=> $12x - \frac{221 x}{20} = 760$
=> $\frac{19 x}{20} = 760$
=> $x = 760 \times \frac{20}{19}$
=> $x = 40 \times 20 = Rs. 800$