A shopkeeper marked up the price of an item by 96% on the actual cost price and allows the discount of 25%. If he gave 2 items free on every dozen purchase, then find the profit percent on sale of 1 dozen items.

Solution

Let’s assume the cost price (CP) of one item is Rs. 100.

Step 1: Calculate the selling price after markup and discount

– After a 96% markup, the price becomes Rs. 196.
– After a 25% discount, the selling price (SP) becomes \(196 \times \frac{3}{4} = Rs. 147\).

Step 2: Calculate the effective selling price for a dozen items with 2 items free

– When 2 items are given free on a dozen, the effective number of items sold is 10.
– Therefore, the effective selling price for a dozen items is \(10 \times 147 = Rs. 1470\).

Step 3: Calculate the cost price for a dozen items

– The cost price for a dozen items is \(12 \times 100 = Rs. 1200\).

Step 4: Calculate the profit and profit percent

– Profit = Selling price for a dozen – Cost price for a dozen = Rs. 1470 – Rs. 1200 = Rs. 270.
– Profit percent = \(\frac{\text{Profit}}{\text{Cost price for a dozen}} \times 100 = \frac{270}{1200} \times 100 = 22.5\%\).

Conclusion

The profit percent on the sale of 1 dozen items is 22.5%.