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A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
- a)10
- b)8
- c)15
- d)7.50
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A man could buy a certain number of notebooks for Rs.300. If each note...
Explanation:
Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
Most Upvoted Answer
A man could buy a certain number of notebooks for Rs.300. If each note...
Let's assume that the man initially bought x notebooks for Rs. 300.
According to the given information, if each notebook cost Rs. 5 more, he could have bought 10 notebooks less for the same amount.
So, if the price of each notebook increased by Rs. 5, the new price of each notebook would be Rs. 5+x.
And if the man bought 10 notebooks less, he would have bought x-10 notebooks.
We can set up the equation based on the given information:
x * 300 = (x - 10) * (5 + x)
Now, let's solve this equation step by step.
Simplifying the equation:
300x = (x - 10)(5 + x)
300x = 5x + x^2 - 50 - 10x
Rearranging the terms:
0 = x^2 - 285x - 50
To solve this quadratic equation, we can either factorize it or use the quadratic formula. Since factoring may not be easy in this case, we will use the quadratic formula.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -285, and c = -50.
Calculating the discriminant:
D = b^2 - 4ac
D = (-285)^2 - 4(1)(-50)
D = 81225 + 200
D = 81425
Since the discriminant is positive, we will have two real solutions.
Calculating the solutions:
x = (-(-285) ± √(81425)) / (2*1)
x = (285 ± √(81425)) / 2
Simplifying further:
x = (285 ± 285.23) / 2
x1 = (285 + 285.23) / 2
x1 = 570.23 / 2
x1 ≈ 285.12
x2 = (285 - 285.23) / 2
x2 = -0.23 / 2
x2 ≈ -0.12
Since the number of notebooks cannot be negative, we can ignore the negative solution.
Therefore, the price of each notebook is approximately Rs. 285.12.
However, none of the given options match this answer.
Hence, there might be an error in the question or the options provided.
According to the given information, if each notebook cost Rs. 5 more, he could have bought 10 notebooks less for the same amount.
So, if the price of each notebook increased by Rs. 5, the new price of each notebook would be Rs. 5+x.
And if the man bought 10 notebooks less, he would have bought x-10 notebooks.
We can set up the equation based on the given information:
x * 300 = (x - 10) * (5 + x)
Now, let's solve this equation step by step.
Simplifying the equation:
300x = (x - 10)(5 + x)
300x = 5x + x^2 - 50 - 10x
Rearranging the terms:
0 = x^2 - 285x - 50
To solve this quadratic equation, we can either factorize it or use the quadratic formula. Since factoring may not be easy in this case, we will use the quadratic formula.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -285, and c = -50.
Calculating the discriminant:
D = b^2 - 4ac
D = (-285)^2 - 4(1)(-50)
D = 81225 + 200
D = 81425
Since the discriminant is positive, we will have two real solutions.
Calculating the solutions:
x = (-(-285) ± √(81425)) / (2*1)
x = (285 ± √(81425)) / 2
Simplifying further:
x = (285 ± 285.23) / 2
x1 = (285 + 285.23) / 2
x1 = 570.23 / 2
x1 ≈ 285.12
x2 = (285 - 285.23) / 2
x2 = -0.23 / 2
x2 ≈ -0.12
Since the number of notebooks cannot be negative, we can ignore the negative solution.
Therefore, the price of each notebook is approximately Rs. 285.12.
However, none of the given options match this answer.
Hence, there might be an error in the question or the options provided.
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A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?a)10b)8c)15d)7.50e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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