The total cost of a washing machine with a toaster was Rs 10500. The toaster was sold at a profit of 22% and the washing machine at a loss of 12%. If the sale price was the same in both the items, then the cost price of the cheaper item was ...............

Let cost price of washing machine = $$Rs. 100x$$

=> Cost price of toaster = $$Rs. (10,500 - 100x)$$

Selling price of toaster (22% profit) = Selling price of washing machine (12% loss)

=> $$\frac{122}{100} \times (10,500 - 100x) = \frac{88}{100} \times 100x$$

=> $$12810 - 122x = 88x$$

=> $$12810 = 88x + 122x = 210x$$

=> $$x = \frac{12810}{210} = 61$$

=> Cost price of washing machine = $$100 \times 61 = Rs. 6100$$

=> Cost price of toaster = $$10,500 - 6,100 = Rs. 4400$$

$$\therefore$$ Toaster is cheaper with cost price = Rs. 4,400