If the price of 1 dozen pen is reduced by RS 6, then 3 more pens will be got at RS 30. Before the reduction of price, calculate the price of 1 dozen pen.

Explanation

Let the price of 1 dozen pen at present is RS x.
`:.` in RS at present `(12)/(x)xx30" pen "=(360)/(x)` pen are got.
If the price is reduced by RS 6 per dozen, then it becomes RS (x-6).
Then for RS 30 we get, `(12)/(x-6)xx30" pens "=(360)/(x-6)` pens.
As per question, `(360)/(x-6)-(360)/(x)=3`.
or, `360((1)/(x-6)-(1)/(x))=3or,120{(x-x+6)/((x-6)x)}=1`
or, `120((6)/(x^(2)-6x))=1`
or, `(720)/(x^(2)-6x)=1or,x^(2)-6x=720`
or, `x^(2)-6x-720=0`
or, `x^(2)-(30-24)x-720=0`
or, `x^(2)-30x+24x-720=0`
or, `x(x-30)+24(x-30)=0`
or, `(x-30)(x+24)=0`
`:.` either `x-30=0" "or,x+20=0`
`impliesx=30" "or,x=-24`.
But price of pens can not be negative, `:.xne-24," ":.x=30`
Hence, before reduction of prices, the price of 1 dozen pen was RS 30.