A shopkeeper purchases two items for Rs. 520. One of them is sold gaining 16% and the other at a loss of 10%, thus making no profit or loss. What is the selling price of the item sold at loss ?

Let cost price of first item = Rs. $$100x$$ and of second item = Rs. $$(520-100x)$$

Profit % on first item = 16%

=> Selling price = $$100x+(\frac{16}{100}\times100x)=Rs.$$ $$116x$$

Similarly, selling price of item sold at 10% loss = $$(520-100x)-\frac{10}{100}\times(520-100x)$$

= $$(520-100x)-52+10x=Rs.$$ $$(468-90x)$$ ------------(i)

Since, there is no profit and no loss, hence total cost price = total selling price

=> $$116x+468-90x=520$$

=> $$26x=520-468=52$$

=> $$x=\frac{52}{26}=2$$

$$\therefore$$ Selling price of the item sold at loss [from equation (i)] = $$468-(90\times2)$$

= $$468-180=Rs.$$ $$288$$

=> Ans - (A)