On selling a tea-set 5% loss and a lemon-set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs. 13. Find the actual price of the tea-set and the lemon-set.

Answer

tea set = ₹ 100, lemon set = ₹ 80

Explanation

Let the cost price of the tea set be ₹ x and that of the lemon set by ₹ y. Then,
` ((95x)/(100) + (115y )/(100)) - ( x + y ) = 7 rArr ((19x + 23 y ))/(20) - (x + y ) = 7`
` " " rArr 3y - x = 140 " " `... (i)
And , ` ((105x )/(100) + (110y)/(100)) - ( x + y ) = 13 rArr ((21 x + 22y ))/(20 ) - (x + y ) = 13`
` rArr x + 2y = 260 " " `... (ii)
Now, solve (i) and (ii).