Question

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.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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