Some students arranged a picnic. The budget for food was Rs 240.Because four students of the group failed to go, the cost of food to each student got increased by Rs 5.Howmany students went for the picnic?
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1 because four students go and five increase
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Let the no.of students be x
Then,amount given by each student=Rs.240/x
If 4 students fail to join the group,no.of students remaining=x-4
Amount of money given by each student=Rs.(240/x+5)
ATQ,
(x-4)(240/x+5)=240
(5 x²+220 x-960)/x=240
5 x²+220 x-960=240 x⇒5 x²+220 x-960-240x=0
5 x²-20 x-960=0⇒x²-4 x-192=0 (dividing the equation by 5)
x²+12 x-16 x-192=0⇒x(x+12)-16(x+12)=0
(x+12)(x-16)=0⇒x+12=0,x-16=0
x=-12,16⇒∴x=16 (neglecting -12)
Hence,there were 16 students.
Then,amount given by each student=Rs.240/x
If 4 students fail to join the group,no.of students remaining=x-4
Amount of money given by each student=Rs.(240/x+5)
ATQ,
(x-4)(240/x+5)=240
(5 x²+220 x-960)/x=240
5 x²+220 x-960=240 x⇒5 x²+220 x-960-240x=0
5 x²-20 x-960=0⇒x²-4 x-192=0 (dividing the equation by 5)
x²+12 x-16 x-192=0⇒x(x+12)-16(x+12)=0
(x+12)(x-16)=0⇒x+12=0,x-16=0
x=-12,16⇒∴x=16 (neglecting -12)
Hence,there were 16 students.
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