Question

after giving two successive discounts each of X percentage on the Marked price of an article total discount is rupees 259.20 if the Marked price of the article is 720 then the value of x is​

Answer 1

Answer:

20

Step-by-step explanation:

Given

Marked price of the article = 720 Rs.

Discount = x%

The first discount on the marked price = $720\times\frac{x}{100}$

New price of the article = $720-720\times\frac{x}{100}=720(1-\frac{x}{100} )$

Second time discount will be on this new price

Thus the new discount price =  $720(1-\frac{x}{100} )(\frac{x}{100} )$

Total Discount = $720(1-\frac{x}{100} )(\frac{x}{100} )+720\times\frac{x}{100}$

                         = $720(\frac{x}{100} )(1-\frac{x}{100} +1)$

                         = $720(\frac{x}{100} )(2-\frac{x}{100})$

But given that total discount = 259.20 Rs.

∴ $720(\frac{x}{100} )(2-\frac{x}{100})=259.20$

⇒ $(\frac{x}{100} )(2-\frac{x}{100})=\frac{259.20}{720}$

⇒ $(\frac{x}{100} )(2-\frac{x}{100})=0.36$

⇒ $(\frac{2x}{100} -\frac{x^{2}}{10000})=0.36$

⇒ $200x-x^{2}=3600$

⇒ $x^{2}-200x+3600=0$

⇒ $x^{2}-180x-20x+3600=0$

⇒ $x(x-180)-20(x-180)=0$

⇒ $(x-180)(x-20)=0$

⇒ $x=180, 20$

But x is a percentage, therefore it cannot be greater than 100

∴ x = 20

Answer 2

Step-by-step explanation:

20

Step-by-step explanation:

Given

Marked price of the article = 720 Rs.

Discount = x%

The first discount on the marked price = 720\times\frac{x}{100}720×

100

x

New price of the article = 720-720\times\frac{x}{100}=720(1-\frac{x}{100} )720−720×

100

x

=720(1−

100

x

)

Second time discount will be on this new price

Thus the new discount price = 720(1-\frac{x}{100} )(\frac{x}{100} )720(1−

100

x

)(

100

x

)

Total Discount = 720(1-\frac{x}{100} )(\frac{x}{100} )+720\times\frac{x}{100}720(1−

100

x

)(

100

x

)+720×

100

x

= 720(\frac{x}{100} )(1-\frac{x}{100} +1)720(

100

x

)(1−

100

x

+1)

= 720(\frac{x}{100} )(2-\frac{x}{100})720(

100

x

)(2−

100

x

)

But given that total discount = 259.20 Rs.

∴ 720(\frac{x}{100} )(2-\frac{x}{100})=259.20720(

100

x

)(2−

100

x

)=259.20

⇒ (\frac{x}{100} )(2-\frac{x}{100})=\frac{259.20}{720}(

100

x

)(2−

100

x

)=

720

259.20

⇒ (\frac{x}{100} )(2-\frac{x}{100})=0.36(

100

x

)(2−

100

x

)=0.36

⇒ (\frac{2x}{100} -\frac{x^{2}}{10000})=0.36(

100

2x

−

10000

x

2

)=0.36

⇒ 200x-x^{2}=3600200x−x

2

=3600

⇒ x^{2}-200x+3600=0x

2

−200x+3600=0

⇒ x^{2}-180x-20x+3600=0x

2

−180x−20x+3600=0

⇒ x(x-180)-20(x-180)=0x(x−180)−20(x−180)=0

⇒ (x-180)(x-20)=0(x−180)(x−20)=0

⇒ x=180, 20x=180,20

But x is a percentage, therefore it cannot be greater than 100

∴ x = 20