Question

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs.90, find the number of articles produced and the cost of each article.

Answer 1

⚘Hey Mate⚘......✍

☃️Solution:✔

We know that,✍

Total Cost of Production = No. of articles produced × Cost of articles.

Given total cost of production = Rs. 90

&

Cost of production of each articles (in rupees) was 3 more than twice the number of articles produced on that day.

Let the number of articles = x ✍

Hence, Cost of articles = 2x + 3✍

Now,✍

Total Cost of Production = Number of articles produced × Cost of articles

I.e.

90 = x(2x + 3)

x(2x + 3) = 90

x(2x) + 3x = 90

2x sq. + 3x = 90

2x sq. + 3x - 90 = 0

We Factorize using,✍

Splitting The Middle Term,

Splitting the middle term Method ✍

we need to find two numbers whose sum = 3

Product = -90 × 2 = - 180

-90 & 2; sum = -88 & product = -180

-9 & 20; sum = 11 & product = -180

-12 & 15; sum = 3 & product = -180

So,✍

2x sq. + 15x -12x - 90 = 0

x(2x + 15) -6(2x + 15) = 0

(x - 6) (2x + 15) = 0

{ x -6 = 0

x = 6

&

2x +15 = 0

2x = -15

x = -15/2 }

So, ✍

x = 6 & x = -15/2

But "x" cannot be negative as number of article is not negative.

Hence, x = 6

Therefore, ✍

Number of articles = x = 6

&

Cost of articles = 2x + 3

= 2(6) + 3

= 12 + 3

= Rs. 15

☄•°• Cost of Articles = Rs. 15✔

☃️Hope it Helps:).................✍

Answer 2

$\sf\blue{Question}$

ᴀ ᴄᴏᴛᴛᴀɢᴇ ɪɴᴅᴜsᴛʀʏ ᴘʀᴏᴅᴜᴄᴇs ᴀ ᴄᴇʀᴛᴀɪɴ ɴᴜᴍʙᴇʀ ᴏғ ᴘᴏᴛᴛᴇʀʏ ᴀʀᴛɪᴄʟᴇs ɪɴ ᴀ ᴅᴀʏ. ɪᴛ ᴡᴀs ᴏʙsᴇʀᴠᴇᴅ ᴏɴ ᴀ ᴘᴀʀᴛɪᴄᴜʟᴀʀ ᴅᴀʏ ᴛʜᴀᴛ ᴛʜᴇ ᴄᴏsᴛ ᴏғ ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ᴏғ ᴇᴀᴄʜ ᴀʀᴛɪᴄʟᴇ (ɪɴ ʀᴜᴘᴇᴇs) ᴡᴀs 3 ᴍᴏʀᴇ ᴛʜᴀɴ ᴛᴡɪᴄᴇ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴀʀᴛɪᴄʟᴇs ᴘʀᴏᴅᴜᴄᴇᴅ ᴏɴ ᴛʜᴀᴛ ᴅᴀʏ. ɪғ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴄᴏsᴛ ᴏғ ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ᴏɴ ᴛʜᴀᴛ ᴅᴀʏ ᴡᴀs ʀs.90, ғɪɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴀʀᴛɪᴄʟᴇs ᴘʀᴏᴅᴜᴄᴇᴅ ᴀɴᴅ ᴛʜᴇ ᴄᴏsᴛ ᴏғ ᴇᴀᴄʜ ᴀʀᴛɪᴄʟᴇ.

$\bf{\underline\pink{Solution}}$

ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴀʀᴛɪᴄʟᴇs ᴘʀᴏᴅᴜᴄᴇs ʙᴇ = x

ᴄᴏsᴛ ᴏғ ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ᴏғ ᴇᴀᴄʜ ᴀʀᴛɪᴄʟᴇ ᴡᴀs= ʀs(2x+3)

$\bf{\underline\green{Given}}$

ᴛᴏᴛᴀʟ ᴄᴏsᴛ ᴏғ ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ɪs ʀs.90

∴$x(2x + 3) = 90$

⇒$2xsq + 3x - 90 = 0$

⇒$2xsq + 15x - 12x - 90 = 0$

⇒$x(2x + 15) -6(2x + 15) = 0$

⇒$(2x + 15) (x - 6) = 0$

⇒$2x + 15 = 0 or x - 6 = 0$

⇒ $x = -15/2 .or .x = 6$

⇒No of articles produced is x

⇒$x = 6$

⇒Hᴇɴᴄᴇ,ɴᴏ ᴏғ ᴀʀᴛɪᴄʟᴇs ᴘʀᴏᴅᴜᴄᴇᴅ ɪs 6

⇒ᴄᴏsᴛ ᴏғ ᴇᴀᴄʜ ᴀʀᴛɪᴄʟᴇ ᴡᴀs 2 x 6 + 3 = 15

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