On selling a tea set at 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 each of the tea set and the lemon set.

Let the actual price of each of the tea set and the lemon set be Rs. x and Rs. y respectively.

According to question -

[ Selling price of tea set(Loss = 5%) + Selling Price of lemon Set(Profit = 15%) ] - [ cost price of tea set + cost price of lemon set ] = Rs. 7

⇒ - 5x + 15y = 700

⇒ - x + 3y = 140.....(1)

and,

[ Selling price of tea set(Profit = 5%) + Selling Price of lemon Set(Profit = 10%) ] - [ cost price of tea set + cost price of lemon set ] = Rs. 13

⇒ 5x + 10y = 1300

⇒ x + 2y = 260.....(2)

Adding equations (1) and (2), we get -

5y = 400

∴ y = 80

Substituting the value of in equation (2), we get -

x = 100

Thus, the cost of tea set = Rs. 100 and the cost of lemon tea = Rs. 80.