Students of 10th standard of a school planned a picnic at the cost of Rs.480.
Had 3 more students join the picnic the cost of the picnic for each student
would have decreased by Rs.8. How many students participated in the picnic.
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15 students participated in the picnic
It is given that the students of 10th standard had planned a picnic at a cost of Rs 480.
Let there initially be x students.
So, each student contributed = Total cost/No. of students
= Rs 480/x
If there were 3 more students, that us (x+3) students,
Cost of picnic for an individual is =
Rs 480/(x+3)
Cost of picnic for an individual has decreased by 8. So,
480/x - 480/(x+3) = 8
⇒ 60/x - 60/(x+3) = 1 [Dividing both sides by 8]
⇒ 60x + 180 - 60x = x(x+3) [Cross multiplying]
⇒ x² + 3x = 180
⇒ x² + 3x - 180 = 0
⇒ x² + 12x - 15x - 180 = 0
⇒ x(x+12) - 15(x+12) = 0
⇒ (x+12)(x-15) = 0
By zero product rule,
x = -12 cant be accepted as no. of students cant be negative.
So, number of students, x = 15
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