sanvi purchased some books for rupees 120.if she purchased 3more book for the same amount each book would have cost rs 2less. find the number of book purchased by sanvi and the price of each book
Answers
The number of books purchased by Sanvi is 12 and the price of each book is Rs. 10.
Step-by-step explanation:
Step 1:
It is given that Sanvi purchased some books for Rs. 120
Let the no. of books purchased by Sanvi be "x".
So,
The cost of each book = Rs. [120/x] ...... (i)
Step 2:
Also given that she purchases 3 more books for the same price
Now, the no. of books with Sanvi will be "(x+3)".
and,
The cost of each book will be = Rs. [120/(x+3)] ...... (ii)
Step 3:
According to the question and substituting the values from (i) & (ii), we get
[120/x] - [120/(x+3)] = 2
⇒ 120 [(x+3-x)/x(x+3)] = 2
⇒ 60 [3/(x² + 3x)] = 1
⇒ 180 = x² + 3x
⇒ x² + 3x - 180 = 0
⇒ x² + 15x - 12x - 180 = 0
⇒ x(x+15) - 12(x+15) = 0
⇒ (x + 15)(x - 12) = 0
⇒ x = - 15 or 12
neglecting the negative value
⇒ x = 12 ← no. of books purchased by Sanvi
∴ The cost of each book = 120/x = 120/12 = Rs. 10
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Step-by-step explanation:
cost of each book be
120÷x
120÷12
10
cost of each book be ₹10
