Question

A shopkeeper purchases 5 chair and 3 tables for rupee 1500. he sold the chair at loss of 15% and the tables at a profit of 19 % this way the total sp os tables was equal to the total spof the chairs find the cp of each chair

Answer 1

Let, CP of chairs = x

And, CP of tables = y

x + y = 1500 (Given)

Loss on chairs = 15%

Total SP of chairs = x - 15%x

= x - (15/100x)

= x - (3/20x)

(Taking LCM of the denominator of x and 3/20x, LCM of 1 (denominator of x) and 20(denominator of 3/20x) = 20 )

= 20x/20 - (3/20x) = 17/20x

Profit on tables = 19%

SP of tables = y + 19/100y

(LCM of 1 (denominator of y) and 100 (denominator of 19/100y) = 100)

= 100y/100 + 19/100y = 119/100y

SP of chairs = SP of tables (Given)

17/20x = 119/100y

x = 119×20/17×100y

= 7×1/5y

= 7/5y

x = 7/5y

x + y = 1500 (Given)

7/5y(Proved) + y = 1500

12/5y = 1500

y = 1500×5/12

y = 125×5 = 625 =

x + y = 1500 (Given)

x + 625(Proved) = 1500

x = 1500 - 625 = 875

SP of chairs = Rs. 875

SP of tables = Rs. 625