Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.

Madhura Khurana · 18th Feb 2019 .

Kilbil Pandey · 18th Feb 2019 .

Let the total no. of students be x.

Cost of food for each = â‚¹ 480/x

When 8 students failed to join, then cost of food for each 480/x – 8

According to question

480/x – 8 - 480/x = 10

480x – 480(x - 8)/x(x – 8) = 10

480(x – x + 8)/x(x – 8) = 10

x2 - 8x – 384 = 0

x2 – 24x + 16x – 384 = 0

(x – 24)(x + 16) = 0

x = 24

The no. of students went for picnic = 24 – 8 = 16

Jasmita Das · 16th Mar 2019 .

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

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