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A certain number of tennis balls were purchased for Rs 450.Five more balls could have been purchased for the same amounts if each ball was cheaper by Rs 15.Find the number of balls purchased.
- a)15
- b)20
- c)10
- d)25
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A certain number of tennis balls were purchased for Rs 450.Five more b...
Let the number of balls purchased be x.
Then, 450/x - 450/x+5 = 15 ⟺ 1/x - 1/x+5 = 15/450 ⟺ x+5-x/x(x+5) = 1/30
⟺ x^2 + 5x - 150 = 0 ⟺ (x + 15) (x - 10) = 0 ⟺ x = 10
Most Upvoted Answer
A certain number of tennis balls were purchased for Rs 450.Five more b...
Given:
Cost of certain number of tennis balls = Rs 450
If each ball was cheaper by Rs 15, then 5 more balls could have been purchased for the same amount.
Let the number of tennis balls purchased be x and the cost of each ball be y.
So, we have two equations:
xy = 450 ....(1)
(x+5)(y-15) = 450 ....(2)
Expanding equation (2), we get:
xy - 15x + 5y - 75 = 450
xy + 5y - 15x = 525 ....(3)
Substituting equation (1) in equation (3), we get:
450 + 5y - 15x = 525
5y - 15x = 75
y - 3x = 15 ....(4)
We need to find the value of x, which represents the number of tennis balls purchased. To do this, we can try different values of x and see which one satisfies all the conditions.
Let's start with x = 10.
Substituting x = 10 in equation (4), we get:
y - 3(10) = 15
y = 45
So, for x = 10, y = 45 and the total cost is 10 * 45 = 450.
Now, let's check if 5 more balls could be purchased for the same amount if each ball was cheaper by Rs 15.
For x = 15, y = 30 and the total cost is 15 * 30 = 450.
And (x+5)(y-15) = 20 * 15 = 300, which is less than 450.
So, x = 10 is the correct answer. Therefore, the number of tennis balls purchased is 10.
Cost of certain number of tennis balls = Rs 450
If each ball was cheaper by Rs 15, then 5 more balls could have been purchased for the same amount.
Let the number of tennis balls purchased be x and the cost of each ball be y.
So, we have two equations:
xy = 450 ....(1)
(x+5)(y-15) = 450 ....(2)
Expanding equation (2), we get:
xy - 15x + 5y - 75 = 450
xy + 5y - 15x = 525 ....(3)
Substituting equation (1) in equation (3), we get:
450 + 5y - 15x = 525
5y - 15x = 75
y - 3x = 15 ....(4)
We need to find the value of x, which represents the number of tennis balls purchased. To do this, we can try different values of x and see which one satisfies all the conditions.
Let's start with x = 10.
Substituting x = 10 in equation (4), we get:
y - 3(10) = 15
y = 45
So, for x = 10, y = 45 and the total cost is 10 * 45 = 450.
Now, let's check if 5 more balls could be purchased for the same amount if each ball was cheaper by Rs 15.
For x = 15, y = 30 and the total cost is 15 * 30 = 450.
And (x+5)(y-15) = 20 * 15 = 300, which is less than 450.
So, x = 10 is the correct answer. Therefore, the number of tennis balls purchased is 10.
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Community Answer
A certain number of tennis balls were purchased for Rs 450.Five more b...
A certain of tennis 450 . five cheaper by rs 15
find the purchase ball of rs 15 number of purchase
450 / 15 = 30
15 by 30
2 plus 8 10ans
find the purchase ball of rs 15 number of purchase
450 / 15 = 30
15 by 30
2 plus 8 10ans
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A certain number of tennis balls were purchased for Rs 450.Five more balls could have been purchased for the same amounts if each ball was cheaper by Rs 15.Find the number of balls purchased.a)15b)20c)10d)25Correct answer is option 'C'. Can you explain this answer?
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