Question

A shopkeeper allows a discount of $10$% to his customers and still gains $20$%. Find the marked price of an article which costs $450$ to the shopkeeper.

Answer 1

Vanitha used this method:
Let M.P. be $100$.
Discount $=10$% of M.P.
$=\frac{10}{100}$ of M.P. $=\frac{10}{100}\times 100$
$=$ $10$
S.P. $=$ M.P. $-$ Discount
$=100-10=$ $90$
Gain $=20$% of C.P.
$=\frac{20}{100}\times 450=$ $90$
S.P. $=$ C.P. $+$ Gain
$=450+90=$ $540$
If S.P. is $90$, then M.P. is $100$.
When S.P. is $540$,
M.P. $=\frac{540\times 100}{90}=$ $600$
$\therefore$ The M.P. of an article $=$ $600$

OR
Vimal used the formula method:
Discount $=10$%, Gain $=20$%,
C.P. $=$ $450$, M.P. $=$ ?
M.P. $=\frac{100+Gain}{100-Discount}\times$ C.P.
$=\frac{(100+20)}{(100-10)}\times 450$
$=\frac{120}{90}\times 450$
$=$ $600$