# Some students planned a picnic.The budget for food was rupees 480.but 8 of them failed to go and, therefore,the cost of food for each member increased by 10.How many students attended the picnic?

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by meenakshiram

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by meenakshiram

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Let the no of students be x

let the cost of each student be y

so xy = 480 ⇒ y = 480/x

so 8 students didn't arrived , each food would have cost rupees 10 more (x-8)(y+10)=480

⇒ (x-8)(480/x+10)=480

⇒ x² - 8x - 384 = 0

⇒ x² + 16x - 24x - 320 = 0

⇒ (x - 24)(x + 16) = 0

so x = - 16 or 24

so number of students can't be negative

so 24 students*ANSWER*

let the cost of each student be y

so xy = 480 ⇒ y = 480/x

so 8 students didn't arrived , each food would have cost rupees 10 more (x-8)(y+10)=480

⇒ (x-8)(480/x+10)=480

⇒ x² - 8x - 384 = 0

⇒ x² + 16x - 24x - 320 = 0

⇒ (x - 24)(x + 16) = 0

so x = - 16 or 24

so number of students can't be negative

so 24 students