Question

by reducing the selling price of an article by rupees 50 a gain of 5% it turns into a loss of of 5% find the original selling price of the article?​

Answer 1

Question -

By reducing the selling price of an article by Rs 50 gain of 5% it turns into a loss of 5%,find the original selling price of the article?

Solution -

Let Rs x be the cost price and Rs y be the selling price of the article

We know that,

Gain= S. P - C. P

= y- x

Now,

$gain\% =( \frac{gain \times 100}{C. P} )$

By putting the values we will get

$5\% = (y - x) \times \frac{100}{x}$

$5 \times \frac{x}{100} = (y - x)$

$\frac{x}{20} = (y - x)$

$x = 20(y - x)$

$x = 20y - 20x$

$x + 20x = 20y$

$21x = 20y$

$y = \frac{21x}{20}$

When the selling price of the article is reduce by Rs 50 then,

$new \: selling \: price( y_{1}) = ( \frac{21x}{20} - 50)$

We know that,

Loss = C. P - S. P

= x - y1

$= x - ( \frac{21x}{20} - 50)$

Now,

$loss\% = ( \frac{loss \times 100}{C. P} )$

By putting the values we will get -

$5 = \frac{x - ( \frac{21x}{20} - 50)}{x} \times 100$

$x = ( \frac{x - 21x}{20} + 50) \times 20$

$x = ( \frac{20x - 21x + 1000}{20} ) \times 20$

$x = - x + 1000$

$x + x = 1000$

$2x = 1000$

$x = \frac{1000}{2}$

$x = 500$

Hence, Cost price of the article is Rs 500

$\therefore \: the \: original \: selling \: price(y) = \frac{21x}{20} \\ = \frac{21 \times 500}{20} \\ =Rs\:\:525$

Answer 2

Answer:

Let Rs x be the cost price and Rsy be the the selling price of the

article.

we know that

Gain%=(

C.P

Gain×100

)

∴5%=(y−x)×

x

100

⇒x=20(y−x)

⇒x=20y−20x

⇒x+20x=20y

⇒21x=20y

⇒y=

20

21x

When the selling price of the article is reduce by Rs50 then the

new selling price of article =Rs(

20

21x

−50)

we know that

Loss%=(

C.P

loss×100

)

5=[

x

x−{

20

21x

−50}

]×100

⇒x={

20

x−21x

+50}×20

⇒x=[

20

{20x−21x+1000}

]×20

⇒x=−x+1000

⇒x+x=1000

⇒2x=1000

So, the cost price of article is Rs500

The original selling price y=

20

21x

=

20

21×500

y=525

The original selling price is Rs 525