by selling a wall clock at a loss of 20% , a shopkeeper incurs a loss of rupees 80 . find it's cost price and selling price .
Answers
Answer:
Loss percent of a wall clock : 20%
Loss rupees of a wall clock : ₹80
To find :
The cost price and the selling price of the wall clock.
Solution :
First, we'll find the value of the cost price.
Let the cost price of the wall clock be y.
Cost price of the wall clock :
\sf \dashrightarrow y - (20\% \: of \: y) = 80⇢y−(20%ofy)=80
\sf \dashrightarrow y - \bigg( \dfrac{20}{100} \: of \: y \bigg) = 80⇢y−(
100
20
ofy)=80
\sf \dashrightarrow y - \bigg( \dfrac{20}{100} \times y \bigg) = 80⇢y−(
100
20
×y)=80
\sf \dashrightarrow y - \bigg( \dfrac{1}{5} \times y \bigg) = 80⇢y−(
5
1
×y)=80
\sf \dashrightarrow y - \dfrac{y}{5} = 80⇢y−
5
y
=80
\sf \dashrightarrow \dfrac{5y - y}{5} = 80⇢
5
5y−y
=80
\sf \dashrightarrow \dfrac{4y}{5} = 80⇢
5
4y
=80
\sf \dashrightarrow 4y = 80 \times 5⇢4y=80×5
\sf \dashrightarrow 4y = 400⇢4y=400
\sf \dashrightarrow y = \dfrac{400}{4}⇢y=
4
400
\sf \dashrightarrow y = 100⇢y=100
Now, we can find the selling price of the clock.
Selling price of wall clock :
\sf \dashrightarrow \dfrac{(100 - Loss\%)}{100} \times CP⇢
100
(100−Loss%)
×CP
\sf \dashrightarrow \dfrac{(100 - 20)}{100} \times 100⇢
100
(100−20)
×100
\sf \dashrightarrow \dfrac{80}{100} \times 100⇢
100
80
×100
\sf \dashrightarrow \dfrac{4}{5} \times 100⇢
5
4
×100
\sf \dashrightarrow \dfrac{4 \times 100}{5} = \dfrac{400}{5}⇢
5
4×100
=
5
400
\sf \dashrightarrow \cancel \dfrac{400}{5} = 80⇢
5
400
=80
Hence, the cost price and the selling price of the wall clock is ₹100 and ₹80 respectively.