Total students planned picnic! The budget for food was 500! But 5 of them did not go and thus the cost of food for each member increased by ₹5! Tell how many students went on?
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let the amount per student be x
therefore 500/x = no. of students in the first case
and so 500/(x+5) gives no. of students in the second case . now.
500/x - 500/(x+5) = 5 (initial - final no. of students)
(500(x+5-x))/(x(x+5))=5
= 2500/(x^2 + 5x)=5
dividing by 5 on each side we get :
500/(x^2 + 5x)=1
= 500=x^2 + 5x
= x^2 + 5x - 500 =0(Quadratic equation )
On solving we get :
x=20 rupees
therefore 500/20 = 25 students
but no. of students went on= 25-5 = 20.
therefore 500/x = no. of students in the first case
and so 500/(x+5) gives no. of students in the second case . now.
500/x - 500/(x+5) = 5 (initial - final no. of students)
(500(x+5-x))/(x(x+5))=5
= 2500/(x^2 + 5x)=5
dividing by 5 on each side we get :
500/(x^2 + 5x)=1
= 500=x^2 + 5x
= x^2 + 5x - 500 =0(Quadratic equation )
On solving we get :
x=20 rupees
therefore 500/20 = 25 students
but no. of students went on= 25-5 = 20.
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By direction options,
500/25 = 20, 500/20 = 25
By mathematical method, the main steps are :
xy=500 ...(i)
and (x−5)(y+5)=500
⇒x−y=5 or y=x−5
Puting in equation (i)
x(x−5)=500
⇒x^2−5x−500=0
⇒x=25 and attended =x−5=20
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