!! Profit Loss tricky solution !! 12 good questions with tricky solution 1. A trader uses a 800gm weight instead of 1 kg. Find his profit %. Soln: (He is buying 800 gm but selling 1000 gm. So, CP is for 800 gm and SP is for 1000 gm.) SP/CP = 1000/800 = 1.25 => 25% profit. 2. A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his profit/loss %. Soln: 1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8 20% increase in price => profit (increase) => 1.2 So, net effect = (0.8) X (1.2) = 0.96 => 4% loss. 3. A milk vendor mixes water to milk such that he gains 25%. Find the percentage of water in the mixture. Soln: To gain 25%, the volume has to be increased by 25%. So, for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt % of water = 0.25 / 1.25 X 100 = 20%. 4. A trader bought an item for Rs. 200. If he wants a profit of 22%, at what price must he sell it? Soln: CP=200, Profit = 22%. So, SP = 1.22CP = 1.22 X 200 = 244/-. 5. A person buys an item at Rs. 120 and sells to another at a profit of 25%. If the second person sells the item to another at Rs. 180, what is the profit % of the second person? Soln: SP of 1st person = CP of 2nd person = 1.25 X 120 = 150. SP of 2nd person = 180. Profit % = SP/CP = 180/150 = 1.2 => 20%. 6. A milk vendor mixes water to 20 lt of milk such that the ratio of milk and water is 4:3. He sold the mixture at Rs. 12 per liter but bought the milk at Rs. 10 per liter. Find the profit % of the vendor. Soln: milk : water = 4:3 => he bought 4 parts (milk) but sold 7 parts (mixture) CP = 10 and SP = 12. So, profit % = (SP/CP) X (SP/CP) = (7/4) X (12/10) = 2.1 => 110% gain. 7. A trader buys some apples at a price of 10 apples for Rs. 8 and sold them at a price of 8 apples for Rs. 10. Find his profit or loss %. Soln: He bought 10 apples for Rs. 8 and sold 8 apples for Rs. 10 => clearly got profit SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625 => 56.25 % gain. 8. A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the CP should be marked on the items? Soln: CP applied with profit = MP applied with discount = SP 1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP. 9. By selling an item at a price a trader gains 40%. What is the profit / loss % if the item is sold at half the price? Soln: SP =1.4CP => (SP/2) = 0.7CP => 30% loss. 10. A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual CP of the article. Soln: 25% gain => SP = 1.25CP…..1. Now, CP is 10% less => 0.9CP and SP is Rs. 2 less => (SP-2). Still, profit is 25% => (SP-2)=1.25(0.9CP) , where SP = 1.25CP (From 1) CP = Rs. 16. 11. A trader gets a discount of 20% from the dealer and marks it at 20% more price then the actual MP to the customer. Find his overall gain %. Soln: Let MP be the price on the item. Then, CP=0.8MP (20% discount) and SP = 1.2MP. So, gain => SP/CP = 1.2/0.8 = 1.5 => 50%. 12. A trader allows a discount of 20% to the customer after marking the item up by 25%. Find his gain/loss% if he is given a commission of 20% of the MP by the dealer. Soln: Trader’s SP = 0.8 X (1.25MP) = MP (since 20% discount on 25% raised price) Trader’s CP = 0.8 MP (20% commission) So, gain = SP/CP = MP/0.8MP = 1.25 => 25%.