Profit, loss and discount
- A trader sells two articles for ₹4,800 each. On one he gains 20% and on the other he loses 20%. What is his overall gain or loss percentage? Answer: D. 4% loss Answer: (D) 4% loss CP of first = 4800/1.2 = 4000 ; CP of second = 4800/0.8 = 6000 . Total CP = 10000, total SP = 9600. L... 1
- Two successive discounts of 20% and 15% are equal to a single discount of: Answer: C. 32% Answer: (C) 32% Single discount = 20 + 15 - 20 × 15/100 = 35 - 3 = 32% . 1
- A shopkeeper marks an article 40% above its cost price and allows a discount of 20% on the marked price. What is his profit percentage? Answer: A. 12% Answer: (A) 12% Let CP = 100. MP = 140. SP = 80% of 140 = 112. Profit = 12%. (Formula: 40 - 20 - 40 × 20/100 = 12% .) 1
- By selling an article for ₹1,140, a man loses 5%. At what price should he sell it to gain 15%? Answer: C. ₹1,380 Answer: (C) ₹1,380 CP = 1140/0.95 = 1200 . SP for 15% gain = 1200 × 1.15 = 1380 . 1
- By selling an article for Rs. 1,512, a shopkeeper gains 12%. At what price (in Rs.) should he sell it to gain 20%? Answer: C. 1620 Answer: (C) 1620 CP = 1512 ÷ 1.12 = Rs. 1,350. For 20% gain, SP = 1350 × 1.2 = Rs. 1,620. 1
- An article is marked at Rs. 2,500. Two successive discounts of 20% and 10% are given on it. What is the selling price (in Rs.)? Answer: D. 1800 Answer: (D) 1800 SP = 2500 × 0.80 × 0.90 = Rs. 1,800. (A single 30% discount would wrongly give Rs. 1,750.) 1
- A shopkeeper marks an article 25% above its cost price and allows a discount of 12% on the marked price. What is his profit percentage? Answer: C. 10% Answer: (C) 10% Take CP = 100. MP = 125, SP = 125 × 0.88 = 110. Profit = 10%. 1
- A trader sells two mobile phones for Rs. 1,200 each. On one he gains 20% and on the other he loses 20%. What is his overall gain or loss percentage? Answer: A. 4% loss Answer: (A) 4% loss CPs: 1200 ÷ 1.2 = 1000 and 1200 ÷ 0.8 = 1500. Total CP = 2500, total SP = 2400. Loss = 100, i.e. 100/... 1
- An article is sold at a loss of 10%. Had it been sold for ₹90 more, there would have been a gain of 5%. What is the cost price? Answer: C. ₹600 Answer: (C) ₹600 Shortcut: the gap between −10% and +5% is 15% of CP = ₹90. CP = 90 × 100 ÷ 15 = ₹600. 1
- An article costs ₹400. At what price must it be marked so that after a discount of 20% the shopkeeper still gains 20%? Answer: D. ₹600 Answer: (D) ₹600 Required SP = 1.2 × 400 = ₹480. SP is 80% of MP, so MP = 480 ÷ 0.8 = ₹600. Shortcut: MP = CP × (100 + gain)... 1
- A man sells two watches at ₹990 each. On one he gains 10% and on the other he loses 10%. What is his overall result? Answer: D. A loss of 1% Answer: (D) A loss of 1% Shortcut: when two items are sold at the same SP with x% gain and x% loss, there is always... 1
- After giving a discount of 10%, a trader still makes a profit of 25%. What is the ratio of the marked price to the cost price? Answer: B. 25 : 18 Answer: (B) 25 : 18 SP = 0.9 × MP = 1.25 × CP, so MP/CP = 1.25/0.9 = 125/90 = 25/18 . MP : CP = 25 : 18. 1
- A shop offers "Buy 4, get 1 free". What is the effective discount percent? Answer: C. 20% Answer: (C) 20% The customer gets 5 items for the price of 4. Discount = 1 item out of 5 = 20%. Trap: 1/4 = 25% divides by th... 1
- A shopkeeper cheats by 20% both while buying and while selling: he takes 20% more goods than he pays for, and gives 20% less than he charges for. What is his overall profit percent? Answer: B. 50% Answer: (B) 50% For ₹100 he receives 120 units of goods. He sells each 80 units as if they were 100. So 120 units bring 120 ×... 1
- The profit earned by selling an article for ₹1,060 equals the loss incurred by selling it for ₹860. At what price should it be sold to make a 25% profit? Answer: D. ₹1200 Answer: (D) ₹1200 Shortcut: CP is midway between the two SPs: (1060 + 860) ÷ 2 = ₹960. SP for 25% profit = 1.25 × 960 = ₹12... 1
- An item marked at ₹8,000 is sold after three successive discounts of 10%, 20% and 25%. What is the selling price? Answer: A. ₹4320 Answer: (A) ₹4320 SP = 8000 × 0.9 × 0.8 × 0.75 = 7200 × 0.6 = ₹4320. Trap: adding the discounts (55%) gives ₹3,600; success... 1
- A sells a bicycle to B at a profit of 20%. B sells it to C at a loss of 10%. If C pays ₹2,160, what did A pay for it? Answer: C. ₹2000 Answer: (C) ₹2000 Shortcut: C's price = A's CP × 1.2 × 0.9 = 1.08 × A's CP. A's CP = 2160 ÷ 1.08 = ₹2000. 1
- By selling 40 metres of cloth, a shopkeeper gains the selling price of 8 metres. What is his profit percent? Answer: D. 25% Answer: (D) 25% SP(40) − CP(40) = SP(8), so CP(40) = SP(32). Shortcut: profit% = 8/40 - 8 × 100 = 25% . Trap: 8/40 = 20% puts... 1
- A shopkeeper allows a discount of 15% on the marked price of ₹1,600 and still gains \(13\frac{1}{3}\%\). What is the cost price? Answer: D. ₹1200 Answer: (D) ₹1200 SP = 85% of 1600 = ₹1360. 131/3% = 2/15 , so SP = 17/15 × CP and CP = 1360 × 15/17 = ₹1200. 1
- When an article is sold at a 20% discount on its marked price, the seller loses 4%. What would his profit percent be if he sold it at the marked price? Answer: A. 20% Answer: (A) 20% 0.8 × MP = 0.96 × CP, so MP = 0.96/0.8 CP = 1.2 CP. Selling at MP gives a profit of 20%. 1
- A dealer marks his goods 40% above the cost price and allows a discount of 25%. He also uses an 800 g weight in place of 1 kg. What is his overall profit percent? Answer: A. 31.25% Answer: (A) 31.25% Let CP = ₹100 per kg. MP = 140, SP after 25% discount = ₹105 for every \"kg\" he sells. But he gives on... 1
- A sells an article to B at a profit of 25%, and B sells it to C at a profit of 20%. C pays ₹225 more than A's cost price. What is A's cost price? Answer: A. ₹450 Answer: (A) ₹450 C pays 1.25 × 1.2 = 1.5 times A's CP. The extra 0.5 × CP = ₹225, so CP = ₹450. 1
- A man buys a certain number of oranges at 3 for ₹5 and the same number at 2 for ₹5. He sells all of them at 5 for ₹12. What is his profit percent? Answer: A. 15.2% Answer: (A) 15.2% Take 6 oranges of each kind (LCM of 3 and 2). Cost = 2 × 5 + 3 × 5 = ₹25 for 12 oranges. SP of 12 oranges... 1
- A trader sells three-fourths of his stock at a profit of 20% and the rest at a loss of 10%. What is his overall profit percent? Answer: C. 12.5% Answer: (C) 12.5% Shortcut (weighted average): 3/4 × 20 + 1/4 × (-10) = 15 - 2.5 = 12.5% . Plain: stock costing ₹100 → ₹75... 1