Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?
Answers
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...
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 planned picnic and 16 attended