Question

a shopkeeper buys a number of book for rs 8000.if he baught 40 more books for the same amount,each book would have cost 10 rs less .how many books did he buy?

Answer 1

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Answer 2

Answer: There are 160 books he bought.

Step-by-step explanation:

Since we have given that

Total amount = Rs. 8000

Let the number of books be 'x'.

Let the cost of each book be 'y'

According to question,

$xy=8000-----(1)$

If he bought 40 more books for the same amount each book would have cost Rs. 10 less.

So, it becomes,

$8000=(x+40)(y-10)----------(2)$

From eq(1) an eq (2) , we have,

$xy=8000=(x+40)(y-10)\\\\xy=xy-10x+40y-400\\\\10x-40y=-400\\\\x-4y=-40$

since we have given that from eq(1),

$y=\frac{8000}{x}\\\\\text{So, our quadratic equation becomes}\\\\x-\frac{8000\times 4}{x}=40=0\\\\x^2+40x-32000=0\\\\x^2+200x-160x-32000=0\\\\x(x+200)-160(x+200)=0\\\\x=-200,160$

Hence, there are 160 books he bought.