Question

some students planned a picnic.the budget for food was rs 480.but eight of these failed to go ant thus the cost of foodbfor each member increased by rs 10.how many students attended the picnic

Answer 1

let the number of students be x
x= 480-(8+10)
NOW SOLVE IT

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 .

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