A room in a hotel had been booked for Rs.1400 for new year celebrations by some boys, but 4 of them failed to reach and each of the rest of the boys had to pay Rs.40 extra. Form a quadratic equation with full explanation. We need to find the number of boys initially.

please provide me this answer

Let the number of boys be n.

Tariff of the hotel room = Rs1400

So, money paid by each student = n/1400 

Now, 4 boys failed to turn up for the celebrations

New number of boys = n - 4

New amount paid by each student = 1400/(n - 4)

Now, we are given that each student have to pay Rs 40 more, when 4 students back out

So, according to the question,

[1400/(n - 4)] - [1400/n] = 40

1400n - 1400n + 5600 / (n² - 4n) = 40

5600 = 40n² - 160n

40n² - 160n - 5600 = 0

dividing both sides by 40

n² - 4n - 140 = 0

n² - 14n + 10n - 140 = 0

n (n - 14) + 10 (n - 14) = 0

(n + 10) (n - 14) = 0

=> n = -10, 14

Since the no. of students cannot be in negative

Hence, number of students = 14

Hope  this helps!!

There's a slight correction in this answer. Here is the actual one

Let the number of boys be n.

Tariff of the hotel room = Rs1400

So, money paid by each student = 1400/n

Now, 4 boys failed to turn up for the celebrations

New number of boys = n - 4

New amount paid by each student = 1400/(n - 4)

Now, we are given that each student have to pay Rs 40 more, when 4 students back out

So, according to the question,

[1400/(n - 4)] - [1400/n] = 40

1400n - 1400n + 5600 / (n² - 4n) = 40

5600 = 40n² - 160n

40n² - 160n - 5600 = 0

dividing both sides by 40

n² - 4n - 140 = 0

n² - 14n + 10n - 140 = 0

n (n - 14) + 10 (n - 14) = 0

(n + 10) (n - 14) = 0

=> n = -10, 14

Since the no. of students cannot be in negative

Hence, number of students = 14

Hope this helps!!

thanks my friend....you solved this