Question

a reduction of 50 paise per dozen in the price of eggs means that a dozen more eggs can be brought for rs 66 find the original price​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Price per dozen of egg = Rs x

Since,

Since, Number of eggs bought for Rs 66.

So, number of egg purchased in dozen be

$\rm :\longmapsto\:n_1 = \dfrac{66}{x}$

Now,

If the price per dozen reduced by 50 paisa.

So, price per dozen = Rs x - 1/2

Since, Number of egg bought for Rs 66.

So, Number of eggs purchased in dozen be

$\rm :\longmapsto\:n_2 = \dfrac{66}{x - \dfrac{1}{2} } = \dfrac{132}{2x - 1} - - - (2)$

According to statement,

A reduction of 50 paise per dozen in the price of eggs, means that a dozen more eggs can be brought for Rs 66.

$\rm :\longmapsto\:\dfrac{132}{2x - 1} - \dfrac{66}{x} = 1$

$\rm :\longmapsto\:\dfrac{132x - 66(2x - 1)}{2x - 1} = 1$

$\rm :\longmapsto\:\dfrac{132x - 132x + 66}{(2x - 1)x} = 1$

$\rm :\longmapsto\:\dfrac{ 66}{(2x - 1)x} = 1$

$\rm :\longmapsto\: {2x}^{2} - x =66$

$\rm :\longmapsto\: {2x}^{2} - x - 66 = 0$

$\rm :\longmapsto\: {2x}^{2} - 12x + 11x - 66 = 0$

$\rm :\longmapsto\:2x(x - 6) + 11(x - 6) = 0$

$\rm :\longmapsto\:(2x + 11)(x - 6) = 0$

$\rm :\implies\:x = 6 \: \: \: x = - \dfrac{11}{2} \: \{ \: rejected \: \}$

So, Price per dozen of eggs is Rs 6.

Answer 2

The original price ​of per dozen eggs is Rs. 60 per dozen.

Step-by-step explanation:

Given:

a reduction of 50 paise per dozen in the price of eggs means that a dozen more eggs can be brought for rs 66.

To Find:

The original price ​of per dozen eggs.

Solution:

As given-

Let  original price of  egg is  Rs. p per dozen.

As given-a reduction of 50 paise per dozen in the price of eggs means that a dozen more eggs can be brought for rs 66.

            Reduction Rate = 50 paise per dozen = Rs.0.50 per dozen

                   1 dozen eggs = 12 eggs

It means.

$66=p+12\times0.50$

$66=p+6$

$p=66-6$

   $= Rs.60\ per\ dozen$

Thus, the original price ​of per dozen eggs is Rs. 60 per dozen.

PROJECT CODE#SPJ2