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Dumbledore enterprises sold a master piece for $45000 then he gains an amount equal to loss when he sold the master piece for $23000. Find the cost price of the master piece.

Dumbledore enterprises sold a master piece for $45000 then he gains an amount equal to loss when he sold the master piece for $23000. Find the cost price of the master piece. Correct Answer 34000

Given 

When, Master piece is sold for $45000 then he gains 

When, Master piece is sold for $23000 then he get loss 

Gain = loss 

Concept used 

SP - CP = Profit

CP - SP = Loss

Calculation 

Let the cost price (c.p) = $ x 

When , he gets loss 

C.p = x - 23000      .......(1)

When , he gets profit/ gain

C.p = 45000 - x        ......(2)

From (1) and (2)

x - 23000 = 45000 - x

⇒ 2x = 68000

⇒ x = 34000

∴ Cost price of the article is $34000

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