Question

If the price of 1 dozen pen is reduced by Rs 6, then 3 more pens will be got in Rs 30. Before the reduction of price, let us calculate the price of 1 dozen pen. ​

Answer 1

Answer:

let the price of 1 dozen pen = x

after reduction, price of 1 dozen pen = x-6

and we know that 1 dozen = 12

so, price of 12 pens = x-6

price of 1 pen = (x-6)/12

then, price of 3 new pens = 30

and by this the price of 1 pen = 30/3 = 10

therefore, 10 = (x-6)/12

x-6 = 120

x = 126

Answer 2

Answer:

The price of 1 dozen pen is Rs 30

Step-by-step explanation:

Let the number of pens bought in Rs 30 be x

Price of 1 pen = 30/x

1 dozen of pens = 12 pens

Cost of one dozen pen = 12 × 30/x = 360/x

If the price of 1 dozen pen is reduced by Rs 6, then 3 more pens will be got in Rs 30.

After the price of 1 dozen pen is reduced by Rs 6,

Number of pens = (x + 3)

New price of each pen = cost of one dozen pen/number of pens

= 360/(x + 3)

According to the question,

$\sf \dfrac{360}{x}-6=\dfrac{360}{x+3} \\\\ \sf \dfrac{360}{x}-\dfrac{360}{x+3}=6 \\\\ \sf 360 \bigg( \dfrac{1}{x} - \dfrac{1}{x+3} \bigg) = 6 \\\\ \sf \dfrac{1}{x} - \dfrac{1}{x+3} = \dfrac{6}{360} \\\\ \sf \dfrac{1(x+3)-1(x)}{x(x+3)} = \dfrac{1}{60} \\\\ \sf \dfrac{x+3-x}{x^2+3x} = \dfrac{1}{60} \\\\ \sf \dfrac{3}{x^2+3x} = \dfrac{1}{60} \\\\ \sf 3(60) = 1(x^2+3x)$

180 = x² + 3x

x² + 3x – 180 = 0

By splitting middle term,

x² + 15x – 12x – 180 = 0

x(x + 15) – 12(x + 15) = 0

(x + 15) (x – 12) = 0

→ x = – 15 ( price can't be negative)

→ x = 12

The original number of pens bought in Rs 30 is 12

Cost of dozen pen = 360/12 = 30