Question

Rs.480 is divided equally among x children.If the number of children were 20 more then each would have got rs 12 less.Find x.

Answer 1

If total rupees to be divided are 480,

Then 》Share of each student=480/x

Now,total children =x+20

》Share of each=480/x+20

Acc to ques

480/x -480/x+20=12

》480(x+20)-480(x)=12(x)(x+20) (Multiply lcm)

》480x + 9600 -480x=12x(x+20)

》9600=12x²+240x

12x²+240x-9600=0

x²+20x-800=0(Divide by 12)

x²+40x-20x-800=0

X(X+40) -20(X+40)=0

(x-20)(X+40)=0

X=20 (negative does not exist)

Hence X=20

Answer 2

Answer:

Share of each child = ₹ 480/x

Now, number of children = x + 20

∵ Share of each child = ₹ 480/x + 20

Now, according to the question

⇒ 480/x – 480/x + 20 = 12

⇒ 480x + 9600 – 480x/x(x + 20) = 12

⇒ 9600 = 12x(x + 20)

⇒ 800 = x2 + 20x

⇒ x2 + 20x – 800 = 0

⇒ x2 + 40x – 20x – 800 = 0

⇒ x(x + 40) - 20(x + 40) = 0

⇒ (x – 20)(x + 40) = 0

⇒ x = 20

or x = - 40 (not possible )

∴ x = 20