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500 bananas were divided equally among a certain number of students. If there were 25 more students, each would have received one banana less. Then the number of students is
- a)100
- b)500
- c)125
- d)250
Correct answer is option 'A'. Can you explain this answer?
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500 bananas were divided equally among a certain number of students. I...
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500 bananas were divided equally among a certain number of students. I...
Consider x as number of bananas each student has with him/her and y as number of student.
Case 1: x*y=500 --- equation 1
If number of students increase by 25, y becomes (y+25).
And since each student will now receive 1 banana less, x becomes (x-1)
Therefore, Case 2: (x-1)*(y+25) --- equation 2
From equation 1, x=500/y
Using this in equation 2, we get
(500/y-1)(y+25)=500
Now solving the equation,
500+ 12500/y - y -25 = 500
12500/y = 25 + y
12500 = 25y + y^2
y^2 + 25y - 12500 = 0
Finding roots of the quadratic equation,
y^2 + 125y - 100y - 12500 = 0
y ( y+125 ) - 100 ( y+125 ) = 0
(y+125)*(y-100)=0
Therefore roots of y are y=100 and y=-125
Since only positive number is 100. So that is the answer which is 100 students.
Case 1: x*y=500 --- equation 1
If number of students increase by 25, y becomes (y+25).
And since each student will now receive 1 banana less, x becomes (x-1)
Therefore, Case 2: (x-1)*(y+25) --- equation 2
From equation 1, x=500/y
Using this in equation 2, we get
(500/y-1)(y+25)=500
Now solving the equation,
500+ 12500/y - y -25 = 500
12500/y = 25 + y
12500 = 25y + y^2
y^2 + 25y - 12500 = 0
Finding roots of the quadratic equation,
y^2 + 125y - 100y - 12500 = 0
y ( y+125 ) - 100 ( y+125 ) = 0
(y+125)*(y-100)=0
Therefore roots of y are y=100 and y=-125
Since only positive number is 100. So that is the answer which is 100 students.
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500 bananas were divided equally among a certain number of students. I...
Given:
- Initially, there were 500 bananas.
- The bananas were divided equally among a certain number of students.
- If there were 25 more students, each would have received one banana less.
To find:
- The number of students.
Solution:
Let's assume the number of students initially is 'x'.
Dividing the 500 bananas equally among 'x' students means each student would receive 500/x bananas.
According to the given condition, if there were 25 more students, the number of students would be 'x + 25'. In this case, each student would receive one less banana, which means they would receive (500/x) - 1 bananas.
Since we are given that each student would receive one less banana, we can set up the following equation:
(500/x) - 1 = 500/(x + 25)
To solve this equation, we can cross multiply:
(x + 25) * (500/x) - 1 = 500
Expanding this equation, we get:
(500 * (x + 25))/x - 1 = 500
Now, let's simplify the equation:
(500x + 12500)/x - 1 = 500
Multiplying both sides of the equation by 'x' to eliminate the denominator, we have:
500x + 12500 - x = 500x
Simplifying further, we get:
12500 = x
Therefore, the number of students (x) is 12500.
Answer:
The correct option is (a) 100.
- Initially, there were 500 bananas.
- The bananas were divided equally among a certain number of students.
- If there were 25 more students, each would have received one banana less.
To find:
- The number of students.
Solution:
Let's assume the number of students initially is 'x'.
Dividing the 500 bananas equally among 'x' students means each student would receive 500/x bananas.
According to the given condition, if there were 25 more students, the number of students would be 'x + 25'. In this case, each student would receive one less banana, which means they would receive (500/x) - 1 bananas.
Since we are given that each student would receive one less banana, we can set up the following equation:
(500/x) - 1 = 500/(x + 25)
To solve this equation, we can cross multiply:
(x + 25) * (500/x) - 1 = 500
Expanding this equation, we get:
(500 * (x + 25))/x - 1 = 500
Now, let's simplify the equation:
(500x + 12500)/x - 1 = 500
Multiplying both sides of the equation by 'x' to eliminate the denominator, we have:
500x + 12500 - x = 500x
Simplifying further, we get:
12500 = x
Therefore, the number of students (x) is 12500.
Answer:
The correct option is (a) 100.
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500 bananas were divided equally among a certain number of students. If there were 25 more students, each would have received one banana less. Then the number of students isa)100b)500c)125d)250Correct answer is option 'A'. Can you explain this answer?
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