Question

The cost of an article goes down every year by 20% of its previous value. find its original cost if the cost it after two years is 19,200 rupees.​

Answer 1

$\LARGE\sf {\underline{\underline\green{Required \:  Answer:-}}}$

Cost of the article at the end of 2nd year = 19,200/-

$\boxed{ \sf{ \implies{The \: cost \: decreases \: every \: year \: by \: 20\%}}}$

Let cost at the beginning of first year be 100.

At the beginning of 2nd year it will be 80/-(i.e. 100 - 20% of 100)

At the beginning of 3rd year = 64/-(80 - 20% of 20)

Thus, an article that costs 100/- will cost 64/- at the 3rd year.

_

The cost of article is 19,200/- after 2 years.

Let the original cost be x.

Thus,

Ratio of the original cost = Ratio of cost after 2 yrs.

$\implies{ \sf{x : 100 = 19,200 : 64}}$

$\sf\implies{ \dfrac{x}{100} = \dfrac{19200}{64} }$

$\sf{ \implies{64x = 19200 × 100}}$

$\sf{\implies{x = \dfrac{19200}{64} }}$

$\boxed{\boxed{= 30,000/-}}$

Thus, the original cost of article was = 30,000/-

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Answer 2

$\LARGE\sf {\underline{\underline\green{Required \:  Answer:-}}}$

Cost of the article at the end of 2nd year = 19,200/-

$\boxed{ \sf{ \implies{The \: cost \: decreases \: every \: year \: by \: 20\%}}}$

Let cost at the beginning of first year be 100.

At the beginning of 2nd year it will be 80/-(i.e. 100 - 20% of 100)

At the beginning of 3rd year = 64/-(80 - 20% of 20)

Thus, an article that costs 100/- will cost 64/- at the 3rd year.

_

The cost of article is 19,200/- after 2 years.

Let the original cost be x.

Thus,

Ratio of the original cost = Ratio of cost after 2 yrs.

$\implies{ \sf{x : 100 = 19,200 : 64}}$

$\sf\implies{ \dfrac{x}{100} = \dfrac{19200}{64} }$

$\sf{ \implies{64x = 19200 × 100}}$

$\sf{\implies{x = \dfrac{19200}{64} }}$

$\boxed{\boxed{= 30,000/-}}$

Thus, the original cost of article was = 30,000/-

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