Question

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1,10fewerofthetowelscouldbeboughtfor$120, excluding sales tax. What is the current price of each towel?

• A. 1$
• B. 2$
• C. 3$
• D. 4$
• E. 12$

Answer 1

The correct option is C 3\Rightarrow$Letnumberoftowelsboughtfor$\$120$ be $n$.

$\Rightarrow$ So price of single towel $=\$\frac{120}{n}$

$\Rightarrow$ Now price of $1$ towel increases by $\$1$

$\Rightarrow$ So, new price of single towel $=\$\frac{120}{n}+1$

$\Rightarrow$ Number of towel that could be bought at this price = $n-10$

$\Rightarrow$ So, new price of single towel = $\frac{120}{(n-10)}$

So, by equating both new price of single towel,

$\Rightarrow$ $\frac{120}{n}+1=\frac{120}{(n-10)}$

$\Rightarrow$ $\frac{(120+n)}{n}=\frac{120}{(n-10)}$

$\Rightarrow$ $n^2-10n-1200=0$

$\Rightarrow$ $(n-40)(n+30)=0$

$\Rightarrow$ $n=40$ or $n=-30$

$\Rightarrow$ Number of towels is $40$.

$\Rightarrow$ Current price per towel = $\frac{120}{40}=\$3$