IIM Bangalore (UGAT) (QA) PYQs

A shopkeeper marks the price of an item $50\%$ above its cost. During a festival, he offers a sequence of discounts — first a $20\%$ discount, then an additional $10\%$ off on the reduced price, and finally gives a further rebate of $₹30$ on the total bill for 10 identical items. If after all these reductions, he still makes a profit of $5\%$ on selling the 10 items, what is the cost price of one item?

In Saroja's sari shop, the marked price of each sari is x% above the cost of its procurement. She sells each sari after a discount of 25%. In addition, if someone buys a dozen saris, she offers an extra sari for free, and still makes a profit of 8% over their cost of procurement. If Saroja had sold the saris without discounting, but with the offer of an extra saree for every dozen sold, then her profit percentage would have been: