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A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount, each book would have cost Re. 1 less. How many books did he buy?
- a)8
- b)16
- c)24
- d)28
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A shopkeeper buys a number of books for Rs. 80. If he had bought 4 mor...
Given, a shopkeeper buys a number of books for Rs. 80.
Let the number of books he bought be x.
Then, the cost of each book = 80/x
According to the question, if he had bought 4 more books for the same amount, each book would have cost Re. 1 less.
So, the new number of books he would have bought = x + 4
And, the cost of each book would be = 80/(x+4)
Also, it is given that each book would have cost Re. 1 less, so we can write:
80/x - 1 = 80/(x+4)
Simplifying this equation, we get:
80x + 320 = 80x - x^2 + 4x
Rearranging and simplifying further, we get:
x^2 - 4x - 320 = 0
Factorizing this quadratic equation, we get:
(x - 20)(x + 16) = 0
So, the possible values of x are 20 and -16. But since x represents the number of books he bought, it cannot be negative. Therefore, x = 20.
Hence, the shopkeeper bought 20 books.
Let the number of books he bought be x.
Then, the cost of each book = 80/x
According to the question, if he had bought 4 more books for the same amount, each book would have cost Re. 1 less.
So, the new number of books he would have bought = x + 4
And, the cost of each book would be = 80/(x+4)
Also, it is given that each book would have cost Re. 1 less, so we can write:
80/x - 1 = 80/(x+4)
Simplifying this equation, we get:
80x + 320 = 80x - x^2 + 4x
Rearranging and simplifying further, we get:
x^2 - 4x - 320 = 0
Factorizing this quadratic equation, we get:
(x - 20)(x + 16) = 0
So, the possible values of x are 20 and -16. But since x represents the number of books he bought, it cannot be negative. Therefore, x = 20.
Hence, the shopkeeper bought 20 books.
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Community Answer
A shopkeeper buys a number of books for Rs. 80. If he had bought 4 mor...
Since number of books cannot be negative, the number of books he initially bought is 16.
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A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount, each book would have cost Re. 1 less. How many books did he buy?a)8b)16c)24d)28Correct answer is option 'B'. Can you explain this answer?
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