Question

Some students of a class planned a picnic . The total budget for picnic is Rs. 75000. But  5 students are unable to pay their share due to financial issues, so other students decided to pay the share of 5 students, thereby the cost of each student who went for picnic increased by Rs. 500. How many students attended the picnic?​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let Total students are : x

Total budget for picnic = 75000/-

share of one student =

$\frac{75000}{x} \:Rs$

Now,According to the situation 5 students were not able to pay.

Now share of each student those who can pay is increased by 500.

Share of each student those who can pay,now

$\frac{75000}{x - 5} \:Rs$

The difference between final share and initial share is 500.

So,

$\frac{75000}{x - 5} - \frac{75000}{x} = 500 \\ \\ take \: LCM\\ \\ 75000\bigg( \frac{x - x + 5}{x(x - 5)}\bigg ) = 500 \\ \\ 150\bigg( \frac{5}{ {x}^{2} - 5x}\bigg ) = 1 \\ \\ 750 = {x}^{2} - 5x \\ \\ {x}^{2} - 5x - 750 = 0 \\ \\ now \: its \: a \: quadratic \: equation \\ \\ {x}^{2} - 30x + 25x - 750 = 0 \\ \\ x(x - 30) + 25(x - 30) = 0 \\ \\ (x - 30)(x + 25) = 0 \\ \\ x - 30 = 0 \\ \\ x = 30 \\ \\ or \\ \\ x + 25 = 0 \\ or \\ x = - 25 \\ \\ discard \: this \: value$

Number of students attended picnic = 30

Verification:

Share of each student =75000/30=2500 Rs

Share of each when 5 don't pay= 75000/25=3000 Rs

Difference (Shared increased)= 500 Rs

Hope it helps you.