Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?
Let the number of students who planned the picnic be ‘a’.
Budget for the food was Rs. 480
Cost of food for each member = 480/a
Given, eight of these failed to go and thus the cost of food for each member increased by Rs. 10
⇒ (a – 8)(480 + 10a) = 480a
⇒ 480a + 10a2 – 3840 – 80a = 480a
⇒ a2 – 8a – 384 = 0
⇒ a2 – 24a + 16a – 384 = 0
⇒ a(a – 24) + 16(a – 24) = 0
⇒ (a + 16)(a – 24) = 0
⇒ a = 24
Number of students who attended the picnic = 24 – 8 = 16
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