Question

Rs. 480 is Divided Equally Among X Children. If the Numbers of Children Were 20 More Then Each Would Have Got Rs. 12 Less. Find ‘X

Answer 1

Step-by-step explanation:

Given :

Rs.480 is divided equally among x children.

If the number of children were 20 more than each would have got Rs.12 less.

To find :

The value of x?

Solution :

Let the required number of children be x.

Then, share of each will be:

• Rs.480/x

New number of children:

• (x + 20)

Share of each now:

• Rs.480/(x + 20)

According to the question:

⇒ 480/x - 480/(x + 20) = 12

⇒ 1/x - 1/(x + 20) = 12/480

⇒ (x + 20) - x/x(x + 20) = 12/480

⇒ x² + 20x - 800 = 0

⇒ x² + 40x - 20x - 800 = 0

⇒ x(x + 40) - 20(x + 40) = 0

⇒ (x + 40) = 0 & (x - 20) = 0

⇒ x = -40 & x = 20

[x ≠ -40, ∵ number of children can't be negative]

∴ The value of x is 20.

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Answer 2

Given : Rs. 480 is divided equally among x children & If the numbers of childrens were 20 more than each would have got Rs. 12 less.

To Find : Find the value of x ?

_________________________

Solution : Let the total no. of children be x.

$~$

• ${\sf{Each~child~gets~=~\dfrac{480}{x}}}$

$~$

◗Increased no. of children = x + 20

$~$

• ${\sf{Each~child~gets~=~\dfrac{480}{x~+~20}}}$

$~$

$\pmb{\sf{\underline{According~ to~ ~the ~Given~Question~:}}}$

$~$

${\sf{Difference~in~share~=~₹ 12}}$

$~$

$\qquad{\sf:\implies{\dfrac{480}{x}~-~\dfrac{480}{x~+~20}~=~12}}$

$\qquad{\sf:\implies{480\Bigg(\dfrac{1}{x}~-~\dfrac{1}{x~+~20}\Bigg)~=~12}}$

$\qquad{\sf:\implies{\dfrac{x~+~20~-~\cancel{x}}{x^2~+~20 x}~=~\cancel\dfrac{480}{12}}}$

$\qquad{\sf:\implies{\dfrac{20}{x^2~+~20 x}~=~\dfrac{40}{1}}}$

$\qquad{\sf:\implies{800~=~x^2~+~20 x}}$

$\qquad{\sf:\implies{x^2~+~20 x~-~800~=~0}}$

$\qquad{\sf:\implies{x^2~+~40 x~-~20 x~-~800~=~0}}$

$\qquad{\sf:\implies{x(x~+~40)~-~20(x~+~40)~=~0}}$

$\qquad{\sf:\implies{(x~-~20)(x~+~40)~=~0}}$

$\qquad{\sf:\implies{x~-~20~=~0~~~~~\bf{\underline{OR}}~~~~~\sf{x~+~40~=~0}}}$

$\qquad{\sf:\implies{x~=~\boxed{\frak{\pink{20}}}~~~~~~~~~~~\bf{\underline{OR}}~~~~~\sf{x}~=~\boxed{\frak{\purple{- 40}}}}}$

$~$

Therefore,

• Since, no. of children be negative, discard is -40.

$~$

Hence,

$\therefore\underline{\sf{The~value~of~x~is~\bf{\underline{20}}}}$