Question

Some students planned a picnic. The budget for the food was 2400. As 8 of them failed to
join the party, the cost of the food for each member increased by ₹ 50. Find how many students
went to the picnic.
answer it quickly​

Answer 1

Question :

Some students planned a picnic. the budget fof the food was ₹ 2400. As 8 of them failed to join the party, the cost of the food for each member increased by ₹ 50. Find how many students went to the picnic.

Solution :

Let,

➡ total no. of students = x

and

➡ cost of the food for each member = y

then,

➛ x y = 2400 ......eqn (1)

➛ x = 2400 / y ...... eqn (2)

_______________________

Now,

since 8 students failed to join the party

therefore,

➡no. of students = x - 8

also,

the cost of food is increased by ₹ 50

so,

➡increased cost of food for each = y + 50

then,

➛ ( x - 8 ) (y + 50 ) = 2400

➛ xy + 50x - 8y -400 = 2400

using eqn (1)

➛ 2400 + 50x -8y -400 = 2400

➛ 50 x - 8 y - 400 = 0

using eqn (2)

➛ 50 (2400/y) - 8y = 400

➛ ( 120000 / y ) - 8y = 400

multiplying by y both sides

➛ 120000 - 8y^2 = 400 y

rearranging the terms

➛ 8 y^2 + 400 y - 120000 = 0

dividing by 8 both sides

➛ y^2 + 50 y - 15000 = 0

splitting the middle term

➛ y^2 + 150 y - 100 y - 15000 = 0

➛ y ( y + 150 ) - 100 ( y + 150 ) =0

➛ ( y-100) (y+150) = 0

so,

y = 100 and y = -150

negative value will be ignored so we will take

y = 100

putting this value in eqn (2)

x = 2400 / 100

x = 24

Hence,

24 students went for picnic.

Answer 2

Answer:

Hence, number of students are 24.