Question

20% of an article is damaged and thrown away and only 20kg is left. Find its orginal weight.

Answer 1

Given :

Weight of left over article : 20 kg

Percent of article damaged : 20%

To find :

The original weight of the article.

Solution :

To find the original weight of the article, first we should find the percent of left over article.

Percent of left over article :

${\sf \dashrightarrow 100 - 20}$

${\sf \dashrightarrow 80\%}$

Now, we can find the original weight of the article

Original weight of the article :

Let the original weight be y,

${\sf \dashrightarrow 80\% \: of \: y = 20}$

${\sf \dashrightarrow \dfrac{80}{100} \times y = 20}$

${\sf \dashrightarrow y = \dfrac{20 \times 100}{80}}$

${\sf \dashrightarrow y = \dfrac{1 \times 100}{4}}$

${\sf \dashrightarrow y = \cancel \dfrac{100}{4} = 25 \: kg}$

Hence, the original weight of the article is 25 kgs.

Verification :

${\sf \dashrightarrow 80\% \: of \: y = 20}$

${\sf \dashrightarrow 80\% \: of \: 25 = 20}$

${\sf \dashrightarrow \dfrac{80}{100} \times 25 = 20}$

${\sf \dashrightarrow \dfrac{4}{5} \times 25 = 20}$

${\sf \dashrightarrow \dfrac{4 \times 25}{5} = 20}$

${\sf \dashrightarrow \dfrac{100}{5} = 20}$

${\sf \dashrightarrow 20 = 20}$

${\sf \dashrightarrow LHS = RHS}$

Answer 2

Answer:

Given :

Weight of left over article : 20 kg

Percent of article damaged : 20%

To find :

The original weight of the article.

Solution :

To find the original weight of the article, first we should find the percent of left over article.

Percent of left over article :

⇢

100

−

20

⇢100−20

⇢

80

%

⇢80%

Now, we can find the original weight of the article

Original weight of the article :

Let the original weight be y,

⇢

80

%

�

�

�

=

20

⇢80%ofy=20

⇢

80

100

×

�

=

20

⇢

100

80

×y=20

⇢

�

=

20

×

100

80

⇢y=

80

20×100

⇢

�

=

1

×

100

4

⇢y=

4

1×100

{\sf \dashrightarrow y = \cancel \dfrac{100}{4} = 25 \: kg}

Hence, the original weight of the article is 25 kgs.

Verification :

⇢

80

%

�

�

�

=

20

⇢80%ofy=20

⇢

80

%

�

�

25

=

20

⇢80%of25=20

⇢

80

100

×

25

=

20

⇢

100

80

×25=20

⇢

4

5

×

25

=

20

⇢

5

4

×25=20

⇢

4

×

25

5

=

20

⇢

5

4×25

=20

⇢

100

5

=

20

⇢

5

100

=20

⇢

20

=

20

⇢20=20

⇢

�

�

�

=

�

�

�

⇢LHS=RHS