Question

some student planned a picnic. the budget for food was rs.480.but 8 of them failed to go and thus the cost of food for each member increased byRS .10.how many attended the picnic

Answer 1

Let the number of students attended the picnic be x

then cost of food for each member = 480/x

the cost of food for each member if 8 students did come = 480/(x+8)

It is given that 480/x = (480/(x+8))+10

[tex] \frac{480}{x} = \frac{10x+560}{x+8} \\ \\ cross \: multiplying \\ \\ 480x+3840 = 10x^{2}+560x \\ \\ \implies 10x^{2}+80x-3840 = 0 \\ \\ x =16[/tex]

16 students attended the picnic

Answer 2

SOLUTION :  

Given : Budget for food =  ₹ 480

Let the number of students planned a picnic be x .

Share of each student = 480/x  

8 students failed to go to picnic , the remaining students = (x - 8)

New share for each student = 480/(x - 8)

480/(x - 8) = 480/x   +  10

480/(x - 8) -  480/x   =  10

480[1/(x - 8) - 1/x ] = 10

1/(x - 8) - 1/x  = 10/480

[x - (x - 8)] / x(x -8) = 1/48

[By taking LCM]

[x - x + 8)] / x² - 8x = 1/48

8/ x² - 8x = 1/48

x² - 8x = 8 × 48

x² - 8x = 384

x² - 8x -  384 = 0

x² + 16x - 24x - 384 = 0

[By middle term splitting]

x(x + 16) - 24(x + 16) = 0

(x - 24)(x + 16) = 0

(x - 24) = 0  or  (x + 16) = 0

x = 24  or x = - 16

Since, number of students can't be negative, so x ≠ - 16  

Therefore , x = 24

The number of students planned a picnic be  24.

Number of students attended the picnic = (x - 8) = 24 - 8 = 16  

Hence, the  number of students attended the  picnic be 16 .

HOPE THIS ANSWER WILL HELP YOU...