# A trademan sold an article at a loss of 20%.Had he sold it for 100 rs more ,he would gain 5%.find cp of article

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by Rocks89

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by Rocks89

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Let the Cost Price of article = CP

He sold it at 20% loss, SP = CP×(100-20 / 100) = 0.8CP

If he had sold it at 5% gain, SP = CP×(100+5 / 100) = 1.05CP

This is Rs. 100 more than 0.8CP

1.05CP - 0.8CP = 100

⇒ 0.25CP = 100

⇒ CP = 100/0.25

⇒ CP = Rs. 400

CP of article is Rs. 400

He sold it at 20% loss, SP = CP×(100-20 / 100) = 0.8CP

If he had sold it at 5% gain, SP = CP×(100+5 / 100) = 1.05CP

This is Rs. 100 more than 0.8CP

1.05CP - 0.8CP = 100

⇒ 0.25CP = 100

⇒ CP = 100/0.25

⇒ CP = Rs. 400

CP of article is Rs. 400

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Let the C.P Of the article be x Rs

with a loss of 20% S.P = C.P - 20% of C.P

S.P = x - (20/100)* x

= x - x/5

=(5x - x)/5

=4x/5

∴S.P = 4x/5 Rs

When S.P is increased by Rs 100 there is a gain of 5%

∴S.P + 100 = C.P+5% of C.P

⇒4x/5 + 100 = x + (5/100)* x

⇒4x/5 - x - x/20 = - 100

⇒(16x - 20x - x)/20 = - 100

⇒ -- 5x = -- 100* 20

⇒ --5x = -- 2000

⇒ x = --2000/ --5

∴ x = 400

∴C.P = 400 Rs.

with a loss of 20% S.P = C.P - 20% of C.P

S.P = x - (20/100)* x

= x - x/5

=(5x - x)/5

=4x/5

∴S.P = 4x/5 Rs

When S.P is increased by Rs 100 there is a gain of 5%

∴S.P + 100 = C.P+5% of C.P

⇒4x/5 + 100 = x + (5/100)* x

⇒4x/5 - x - x/20 = - 100

⇒(16x - 20x - x)/20 = - 100

⇒ -- 5x = -- 100* 20

⇒ --5x = -- 2000

⇒ x = --2000/ --5

∴ x = 400

∴C.P = 400 Rs.