The total cost of a stove with cooker was Rs 13,125. The cooker was sold at a profit of 30% and the stove at a loss of 20%. If the sale price was the same in both the items, then the cost price of the cheaper item was

Let cost price of stove = $$Rs. 100x$$

=> Cost price of cooker = $$Rs. (13,125 - 100x)$$

Selling price of cooker (30% profit) = Selling price of stove (20% loss)

=> $$\frac{130}{100} \times (13,125 - 100x) = \frac{80}{100} \times 100x$$

=> $$17062.5 - 130x = 80x$$

=> $$x = \frac{17062.5}{210} = 81.25$$

=> Cost price of stove = $$100 \times 81.25 = Rs. 8,125$$

=> Cost price of cooker = $$13,125 - 8,125 = Rs. 5,000$$

$$\therefore$$ Cooker is cheaper with cost price = Rs. 5,000