Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The price would be rs 30

Step-by-step explanation:

Consider x be the original number of pen bought in rs 30.

So the original price of each pen = $\frac{\text{Total price}}{\text{Total pens}}$

$=\frac{30}{x}$

∵ 1 dozen = 12 units

Thus, the original price of 1 dozen pen = 12 × price of each pen

$= 12\times \frac{30}{x}$

$= \frac{360}{x}$

Now, if number of pen is increased by 3,

New number of pen = x + 3,

Then price of each pen = $\frac{30}{x+3}$,

Thus, the new price of 1 dozen pen = $12\times \frac{30}{x+3}$

$=\frac{360}{x+3}$

According to the question,

$\frac{360}{x}-\frac{360}{x+3}=6$

$\frac{360x+1080 - 360x}{x^2+3x}=6$

$\frac{1080}{x^2+3x}=6$

$\frac{180}{x^2+3x}=1$

$180 = x^2 + 3x$

$\implies x^2 + 3x- 180=0$

By middle term splitting,

$x^2 + 15x - 12x - 180=0$

$x(x+15)-12(x+15)=0$

$(x-12)(x+15)=0$

By zero product property,

x = 12 or x = -15 ( not possible ),

Thus, the original number of pen = 12,

And, the price  of 1 dozen pen before the reduction of price = $\frac{360}{12}$

= 30

#Learn more:

Find the ratio of the price of a pen to that of a ball pen when pens costs is Rs.144 per dozen and ball pen costs Rs.80 score

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