Question

A man sold a table and chair together for rupees 850 at a loss of 10% on the table and a gain of 10% on the chair by selling from together for rupees 950 he would made a gain of 10% on the table and loss of 10% on the chair find the cost price of each

Answer 1

let the cost of the chair be 'x' and the cost of the table be 'y’
in case 1
gain on chair = (10/100) *x
                       = x/10
loss on table = (10/100) * y
                      = y/10
⇒ (x + x/10) + (y - y/10) = 850
⇒ (11x/10) + (9y/10) = 850
⇒ 11x + 9y = 8500............... 1
in case 2
⇒ (x - x/10) + (y + y/10) = 950
9x + 11y = 9500 ................. 2
after solving equations 1 and 2 we will get
x = 200 and y = 700
∴cost of the chair is Rs 200 and the cost of the table is Rs 700

Answer 2

let the cost of the chair be x and the cost of the table be y 
gain of chair[10/100]xX = X/10
loss of table[ 10 / 100] xY = y/10
=( x + x/ 10 ) + ( y- y/10 ) = 850
= ( 11x/10) + ( 9y / 10 ) = 850
=11x + 9y = 8500--------- i eq
( x- x/10) + (y+ y/10) = 950
9x +11 y = 9500---------- ii eq
solving i and ii we get
x=200 and y = 700