Question

By selling an article at 20% discount, a
shopkeeper gains 25%. If the selling price of
the article is 1,440; find :
(i) the marked price of the article.
(ii) the cost price of the article​

Answer 1

Answer:

i. let mp be x

so sp is 1440

discount= 20/100×x

discount =x/5

mp=sp+discount

x=1440-x/5

x-x/5=1440

5x-x/5=1440

4x/5=1440

x=1440×5/4

x=1800

mp= 1800

ii. let cp be x

sp=1440

gain=25%

gain=25/100×x

gain=x/4

cp=sp-gain

x=1440-x/4

x-x/4=1440

4x-x/4= 1440

3x/4=1440

x=1440×4/3

thus cp= 1920

Answer 2

Given that,

Discount percent is 20%.

Selling price of article is 1440.

Gain percent is 25%.

(i) The market price of the article.

Discount percent = 20%.

Selling price = 1440

Discount = Market price - Selling price

= M.P - 1440 [Here, M.P is market price]

Discount is M.P - 1440.

$\boxed{\bold{Discount \: percent = \cfrac{Discount}{M.P} \times 100}}$

➝ M.P - 1440/M.P × 100 = 20

➝ (M.P - 1440) × 100 = 20 × M.P

➝ M.P - 1440 = 20/100 × M.P

➝ M.P - 1440 = M.P/5

➝ 5 × (M.P - 1440) = M.P

➝ 5 M.P - 7200 = M.P

➝ 5 M.P = M.P + 7200

➝ 5 M.P - M.P = 7200

➝ 4 M.P = 7200

➝ M.P = 7200/4

➝ M.P = 1800

Therefore,

Market price of article is 1800.

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(ii) The cost price of article.

Gain percent = 25%

Selling price = 1440

Gain = Selling price - Cost price

= 1440 - C.P [Here, C.P is cost price]

Gain is 1440 - C.P

$\boxed{\bold{Gain \: percent = \cfrac{Gain}{C.P} \times 100}}$

➝ 25 = 1440 - C.P/C.P × 100

➝ 25 × C.P = (1440 - C.P)× 100

➝ 25/100 × C.P = 1440 - C.P

➝ C.P/4 = 1440 - C.P

➝ C.P = 4×(1440 - C.P)

➝ C.P = 5760 - 4 C.P

➝ 4 C.P + C.P = 5760

➝ 5 C.P = 5760

➝ C.P = 5760/5

➝ C.P = 1152

Therefore,

Cost price of article is 1152.