IIM Bangalore (UGAT) (QA) PYQs

An article costing ₹80 was marked 25% above the cost price. After offering a discount of X%, the customer now pays ₹81. If the marked price is increased twice successively by X% and the article is sold at the new marked price, then the profit would be what percent more than the profit when the selling price was ₹81?

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?