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Question
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
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Solution
Let x students planned a picnic.
Then, the share of each student `= 500/x`
According to question, 5 students fail to go picnic, then remaining students = (x - 5).
Therefore, new share of each student `500/(x-5)`
It is given that
`500/(x-5)-500/x=5`
`(500x-500x+2500)/((x-5)x)=5`
`2500/(x^2-5x)=5`
2500 = 5(x2 - 5x)
`2500/5=x^2-5x`
500 = x2 - 5x
x2 - 5x - 500 = 0
x2 + 20x - 25x - 500 = 0
x(x + 20) - 25(x + 20) = 0
(x + 20)(x - 25) = 0
x + 20 = 0
x = -20
Or
x - 25 = 0
x = 25
Because x cannot be negative.
Thus, the total numbers of students attend a picnic
= x - 5
= 25 - 5
= 20
Therefore, the total numbers of students attend a picnic be x = 20.
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