Question

A man sells two wrist watches at $594$ each. On one he gains $10$% and on the other he loses $10$%. Find his gain or loss percent on the whole.

Answer 1

Given : S.P. of the first wrist watch $=$ $594$, Gain% $=10$%
$\therefore$ C.P. of the first wrist watch $=\frac{100}{100+profit}\times$S.P.
$=\frac{100}{(100+10)}\times 594$
$=\frac{100}{110}\times 594=$ $540$.
Similarly, C.P. of the second watch on which he loses $10$% is
$=\frac{100}{(100-Loss)}\times$ S.P.
$=\frac{100}{(100-10)}\times 594=\frac{100}{90}\times 594=$ $660$.
To say whether there was an overall Profit or Loss, we need to find the combined C.P. and S.P.
Total C.P. of the two watches $=540+660=$ $1,200$.
Total S.P. of the two watches $=594+594=$ $1,188$.
Net Loss $=1,200-1,188=$ $12$.
Loss% $=\frac{Loss}{C.P.}\times 100$
$=\frac{12}{1200}\times 100=1$%.