Question

Some students planned a picnic. The budget for food was Rs. 480. But 8 of these faied to go & thus cost of food for each member increased by Rs. 10. How many students attended the picnic

Answer 1

let the no of students be x
let the cost of each student be y

so xy = 480 ⇒ y = 480/x

so 8 students didn't arrived , each food would have cost rupees 10 more (x-8)(y+10)=480

⇒ (x-8)(480/x+10)=480

⇒ x² - 8x - 384 = 0

⇒ x² + 16x - 24x - 320 = 0

⇒ (x - 24)(x + 16) = 0

so x = - 16 or 24

so number of students can't be negative
so 24 students ANSWER

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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