Question

The cost of some books is 60 rupees. Cost of every book is same. If cost of book is decrease by 1 rupee, one gets 5 books more for some amount.
What is cost of each book & how many books
are purchased?..
please give me step by step and correct answer...
I will mark them brainliest....​

Answer 1

✬ Number of books = 15 ✬

✬ Cost of each book = Rs 4 ✬

Step-by-step explanation:

Given:

• Cost of some books is Rs 60.
• Cost of every book is same.
• If cost of book is decreased by 1 then one get 5 more book for same amount.

To Find:

• What is cost of each book and how many books are purchased ?

Solution: Let the cost of each book be Rs x and number of books be y. Therefore,

➨ Total cost of books = Rs 60

➨ x × y = 60.........i

➨ y = 60/x ..........ii

[ Now cost of book is decreased by Rs 1 ]

∴ New price = (x – 1)

A/q

• After decreasing cost of book by one then number of book purchased is increased by 5.

• Number of books = (y + 5)

$\implies{\rm }$ (y + 5) (x – 1) = 60

$\implies{\rm }$ y(x – 1) + 5(x – 1) = 60

$\implies{\rm }$ xy – y + 5x – 5 = 60

$\implies{\rm }$ 60 – 60/x + 5x – 5 = 60

$\implies{\rm }$ 5x – 60/x – 5 = 0

$\implies{\rm }$ 5(x – 12/x – 1) = 0

$\implies{\rm }$ x – 12/x – 1 = 0

Now taking LCM

➮ x² – 12 – x/x = 0

➮ x² – x – 12

Now using middle term splitting method

➮ x² – 4x + 3x – 12

➮ x(x – 4) + 3(x – 4)

➮ (x + 3) or (x – 4)

➮ x = – 3 or x = 4

• We will take positive value of x i.e 4.

Now put the value of x in equation ii.

➮ y = 60/4 = 15

Hence, cost of each book is Rs 4 and number of books purchased is 15.

Answer 2

ɢɪᴠᴇɴ:-

• The cost of some books is 60 rupees.
• Cost of every book is same.
• If cost of book is decrease by 1 rupee, one gets 5 books more for some amount.

ᴛᴏ ғɪɴᴅ:-

• Cost of each book
• Number of books purchased

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

Let the number of books be "x"

Total cost of the books = Rs 60

Cost of 1 book = 60 ÷ x  = $\dfrac{60}{x}$

New Price = $\dfrac{60}{x}$ - 1

Cost of book decreased by Rs 1, number of purchase increased by 5

($\dfrac{60}{x}$- 1)(x + 5) = 60

60 + $\dfrac{300}{x}$- x - 5 = 60

$\dfrac{300}{x}$ - x - 5 = 0

300 - x² - 5x = 0

x² + 5x - 300 = 0

(x - 15)(x + 20) = 0

x = 15 or x = -20 (rejected, since books purchased cannot be negative)

❀Number of books = x = 15

$\sf\green{↬}$Total cost = Rs 60

$\sf\purple{↬}$Number of books = 15

$\sf\red{↬}$Cost of a book = 60 ÷ 15 = Rs 4

Hence, each book costs Rs 4 and 15 books are purchased.

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