Question

The total cost price of a certain number of identical articles is Rs.4800.By selling the articles at Rs.100 each,a profit equal to the cost price of 15 articles is made.Find the number of articles bought.

Answer 1

Hey

Here is your answer,

Given : The total cost price of a certain number of identical articles is Rs 4,800 .

Let , Total number of articles bought = x , So

Cost price of a article = 4800/x

Also given : By selling the articles at Rs 100 each , a profit equal to the cost price of 15 articles is made .So we get

100 x − 4800= 15 × 4800/x
⇒100 x − 4800= 72000/x
⇒100 x −72000/x− 4800=0
⇒100 x2 − 72000 − 4800 x / x=0
⇒ 100 x 2 - 4800 x - 72000 = 0
⇒ 100 x 2 - 4800 x - 72000 = 0
⇒ 100( x 2 - 48 x - 720 ) = 0
⇒x 2 - 48 x - 720= 0
⇒x 2 - 60 x + 12 x - 720 = 0
⇒x ( x - 60 ) + 12 ( x - 60 ) = 0
⇒( x + 12 )( x - 60 ) = 0
So,

x = - 12 and 60 , We assume ' x ' as number of article so that can't be negative . So we get

x = 60

Therefore,

The number of articles he bought = 60

Hope it helps you!

Answer 2

Answer: 60

Step-by-step explanation:

Let , Total number of articles bought = x , So

Cost price of a article = 4800/x

Also given : By selling the articles at Rs 100 each , a profit equal to the cost price of 15 articles is made .So we get

100 x − 4800= 15 × 4800/x

⇒100 x − 4800= 72000/x

⇒100 x −72000/x− 4800=0

⇒100 x2 − 72000 − 4800 x / x=0

⇒ 100 x 2 - 4800 x - 72000 = 0

⇒ 100 x 2 - 4800 x - 72000 = 0

⇒ 100( x 2 - 48 x - 720 ) = 0

⇒x 2 - 48 x - 720= 0

⇒x 2 - 60 x + 12 x - 720 = 0

⇒x ( x - 60 ) + 12 ( x - 60 ) = 0

⇒( x + 12 )( x - 60 ) = 0

So,

x = - 12 and 60 , We assume ' x ' as number of article so that can't be negative . So we get

x = 60