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.

Question

Philoid · Accepted Answer

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.