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Question
Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.
Solution
Let the total number of students be x.
Total oranges = 540
Orange each student gets will be `540/x`.
If 30 more students are there so, the total number of students will be x + 30.
Number of oranges per person will be `540/(x + 30)`.
If 30 students were more each would get 3 oranges less = `540/x - 3`
`540/(x + 30) = 540/x - 3`
⇒ `3 = 540(1/x - 1/(x + 30))`
⇒ `1 = 540/3 ((x + 30 - x)/(x(x + 30)))`
⇒ `1 = 180 ((30)/(x^2 + 30x))`
⇒ x2 + 30x = 5400
⇒ x2 + 30x − 5400 = 0
⇒ x2 + 90x − 60x − 5400 = 0
⇒ x(x + 90) − 60(x + 90) = 0
⇒ (x + 90)(x − 60) = 0
⇒ x + 90 = 0 or x – 60 = 0
⇒ x = – 90 or x = 60
But number of students cannot be negative so, the number of students is 60.
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