Profit and Loss 2

PROFIT AND LOSS SEBASTIAN VATTAMATTAM 1. Introduction Cost Price: CP Selling Price: SP Profit: P = SP − CP Loss: L = CP − SP Profit Percent: P CP × 100 Loss Percent: L CP × 100 2. Revision Problem 2.1. A bookseller buys 50 books at Rs 38 each and sells them at Rs 54 each. How much profit does he make altogether? Hint: Method 1 CP = Rs50 × 38 = 1900 SP = Rs50 × 54 = 2700 P = SP − CP = Rs.800 Method 2 Profit on one book = SP − CP = 54 − 38 = 16 Total Profit = Rs50 × 16 = 800 Problem 2.2. A man buys 10 eggs for Rs 2.25 each and sells them for a total of Rs 27. How much profit or loss does he make? Date: 28-March-2010. 12 SEBASTIAN VATTAMATTAM Total CP = 10 × 2.25 = 22.5 Total SP = 27 P = SP − CP = 4.50 Problem 2.3. A man buys a dozen notebooks for Rs234 and makes a loss of Rs0.75 on each. What is the selling price of each notebook?CP = Rs.234 For each CP = 234 12 = 19.50 For each L = 0.75 For each SP = 19.50 − 0.75 = 18.75 Problem 2.4. A woman buys 200 eggs at 5 for Rs 15. She sells them all at Rs 4 each. How much profit does she make? CP = 15 5 × 200 = 600 SP = 200 × 4 = 800 P = SP − CP = 200 Problem 2.5. A carpenter makes a table and sells it for Rs 3060. The materials cost him Rs.1286 and labour cost him Rs.1047.75. What is his profit? SP = 3060 CP = 1286 + 1047.75 = 2333.75 P = SP − CP = 3060 − 2333.75 = 726.25PROFIT AND LOSS 3 Problem 2.6. A book-shop buys 200 books at Rs 37 each. A half of these are sold at Rs 40, a quarter are sold at Rs 41 and the rest at Rs 43. What is the profit? CP = 200 × 37 = 7400 SP = 100×40+50×41+50×43 = 4000+2050+2150 = 8200 P = SP − CP = 800 Problem 2.7. The marked price of a suit is Rs 300. If 10 % discount is allowed, what is the sale price? Discount D = 300 × 10 100 = 30 Sale Price = 300 − 30 = 270 Problem 2.8. The marked price of a bicycle is Rs 456.50. If a discount of 9% is allowed, what is the sale price? Discount D = 456.50 × 9 100 = 41.085 Sale Price = 456.50 − 41.085 = 415.42 Problem 2.9. A book is bought for Rs 32 and sold for Rs 40. Find the profit percentage. CP = 32 SP = 40 P = SP − CP = 8 Profit Percent = 8 32 × 100 = 25%4 SEBASTIAN VATTAMATTAM Problem 2.10. A bicycle is bought for Rs 800 and sold for Rs 600. Find the loss percentage. CP = 800 SP = 600 Loss Percent = 200 800 × 100 = 25% 3. Harder Problems Problem 3.1. Sunil purchased equal number of two types of oranges at 4 and 6 per rupee respectively. He sold both types at 10 for Rs.2. Find the percentage of profit or loss he makes. Total number of oranges = 2x CP = x4 + x6 = 5x 12 SP = 2 10 × 2x = 2x 5 CP = 25x 60 , SP = 24x 60 ) L = x 60 Loss percent = x 60 25x 60 × 100 = 4% Problem 3.2. A shopkeeper agrees to sell sugar at the cost price. But, by using false weights, he gains 25%. How much does he give instead of 1 kg of sugar? Total quantity = 1000gm Let CP = 100 P = 25 Sugar kept back = xgmPROFIT AND LOSS 5 P = x 1000 × 100 = x 10 = 25 ) x = 250 Sugar handed over = 1000 − 250 = 750gm Problem 3.3. A tradesman, using a false balance defrauds to the extend of 10 % in buying goods and also defrauds 10 % in selling. Find the net gain percent. Total quantity bought = 100kg Obtained = 110kg Total sold = 110kg Kept back = 110 × 10 100 = 11kg CP = 100, P = 11% Problem 3.4. A man sells two horses at the same price. On one he makes 10 % profit and on the other he suffers 10% loss. Find the percentage of profit or loss he makes. Total CP = 100 First Horse: CP = x, P = x × 10 100 = x 10 ) SP = 11x 10 Second Horse CP = 100 − x L = (100 − x) 10 100 = 100 − x 106 SEBASTIAN VATTAMATTAM SP = 100 − x − 100 − x 10 = 9 10(100 − x) Given: 11x 10 = 9 10(100 − x) ) x = 45 Total SP = 2 × 11x 10 = 99 Loss percent = 1% Problem 3.5. Successive discounts of p% and q % are made on an article for sale. Find the net discount percenttage Marked price = 100 First sale price = 100 − p Second discount = (100 − p) q 100 Second Sale price = (100 − p) − (100 − p) q 100 = (100 − p)(100 − q) 100 Effective discount percent = 100 − (100 − p)(100 − q) 100 = p + q − pq 100 Problem 3.6. If a man purchases 11 oranges for Rs10 and sells 10 oranges for Rs11 how much profit or loss does he make. CP = 10, SP = 11 10 × 11 = 12.10, P = SP − CP = 2.10PROFIT AND LOSS 7 Problem 3.7. A man purchases 8 pens for Rs.9 and sells 9 pens for Rs 8 how much profit or loss does he make. CP = 9, SP = 89 × 8 = 7.11, L = 9 − 7.11 Problem 3.8. A boy purchases oranges at 9 for Rs.16 and sells them at 11 for Rs.20. What does he gain or lose perceent CP = 16, SP = 20 11×9 = 180 11 , P = 180 11 −16 = 4 11, P% = P CP ×100 Problem 3.9. A man purchases a certain no of toffees at 25 a rupee and the same no at 20 a rupee. He mixes them together and sells at 45 for Rs 2. What does he gain or lose percent in the transaction. Number of toffees = 2x,CP = 1 25x + 1 20x = 9x 100, SP = 2 452x = 4x 45 , L = x 900, L% = L CP × 100 Problem 3.10. Oranges are bought at 11 for a rupee and equal no more at 9 for a rupee. If these are sold at 10 for a rupee, find the gain or loss percent. CP = 1 11x + 19x, SP = 1 102x Mary Bhavan, Ettumanoor, Kerala, INDIA E-mail address: vattamattam@gmail.com