Question

A shopkeeper sold an article at a gain of 5% .If he had sold it for rs 16.50 less ,he would have loss 5% .Find the cp of the article

Answer 1

$<b>Heya mate. (^_-). Solution below.$
====================================

• Let the cost price (C.P) be x.



[] In first case,

C.P. = x

Gain % = 5 %


•°• Selling price (S.P),

= (100 + gain%) × C.P/100

= (100 + 5) × x/100

= 105 × x/100

= 105x/100



[] In second case,

C.P = x

Loss % = 5%


•°• S.P,

= (100 - loss%) × C.P/100

= (100 - 5) × x/100

= 95 × x/100

= 95x/100




[] Now, according to the question, if he had sold the article for 16.50 Rs. less, he could have suffered a loss of 5% instead of gaining 5%.

or, S.P at 5% gain - 16.50 = S.P at 5% loss

=> 105x/100 - 16.50 = 95x/100

=> 105x/100 - 95x/100 = 16.50

=> (105x - 95x)/100 = 16.50

=> 10x/100 = 16.50

=> x = 16.50 × 100/10

=> x = 1650/10

=> x = 165

[] Therefore, C.P = x = 165.

$<marquee>Hence, cost price of the article is 165 Rs.</marquee>$
====================================

Thank you... ;-)