a man buys an article for rs x and sold it for rs 56 at a gain of x%.find the value of x

Cost price = Rs x 
Selling price = Rs 56
Profit = 56-x (SP-CP) 
Profit % = x % 

Now, we know Cost Price = (100/100+P%) (SP) 

CP, x = (100/100+x) (56) 
=> x = 5600 / 100 + x 
=> 100x + x² = 5600 
=> x² + 100x - 5600 = 0
=> x² + 140x - 40x - 5600 = 0
=> x(x+140) - 40(x+140) = 0
=> x-40 = 0  ;  x+140=0
=> x = 40  ;  x = -140

Since the C.P. cannot be negative, 
x = 40 Rs. 
x% = 40 %


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