Question

A dealer allows a discount of $10$% and still gains $10$%. What is the cost price of the book which is marked at $220$?

Answer 1

Sugandan used this method:
M.P. $=$ $220$.
Discount $=10$% of M.P.
$=\frac{10}{100}\times 220=$ $22$
S.P. $=$ M.P. $-$ Discount
$=220-22=$ $198$
Let C.P. be $100$.
Gain $=10$% of C.P.
$=\frac{10}{100}\times 100=$ $10$
S.P. $=$ C.P. $+$ Gain
$=100+10$
$=$ $110$.
If S.P. is $110$, then C.P. is $100$.
When S.P. is $198$,
C.P. $=\frac{198\times 100}{110}$
$=$ $180$.

OR

Mukundan used the formula method:
Discount $=10$%
Gain $=10$%
M.P. $=$ $220$
C.P. $=\frac{100-Discount}{100+Gain}\times$ M.P.
$=\frac{100-10}{100+10}\times 220$
$=\frac{90}{110}\times 220=$ $180$.