Answer VerifiedHint: In this particular question use the concept that the cost price of the (1/3) goods is equal to the cost price of the whole goods divide by 3 and the selling price of the (1/3) goods = cost price of the (1/3) goods – 10% of cost price of the (1/3) goods so use these concepts to reach the solution of the question. Complete step-by-step answer: Given data:Cost price of the goods = Rs. 450Cost price of the (1/3) goods = cost price of the whole goods divided by 3.So, the cost price of the (1/3) goods = (450/3) = 150 Rs.So the cost price of the remaining goods = 450 – 150 = 300 Rs.Now it is given that (1/3) of the goods is sold at 10% loss.So the selling price of the (1/3) goods = cost price of the (1/3) goods – 10% of the cost price of the (1/3) goods.So the selling price of the (1/3) goods = 150 - $ \left( {\dfrac{{10}}{{100}}} \right)150 $ Therefore, 150 – 15 = 135 Rs.Now we have to gain overall 20% on the whole transaction.So the 20% of the Rs. 450 = $ \left( {\dfrac{{20}}{{100}}} \right)450 = 90 $ Rs.But he has lost Rs. 15 in the first transaction.So overall he has to sell the remaining goods at a profit of (90 + 15) = 105 Rs.Cost price of the remaining goods = 300 Rs.So the selling price of the remainder goods must be = cost price of the remainder goods + overall profitSo the selling price of the remaining goods = 300 + 105 = 405 Rs.Now the gain percentage is the ratio of the difference of the selling and the cost price to the cost price multiplied by 100.So the gain percentage = $ \dfrac{{{\text{selling price - cost price}}}}{{{\text{cost price}}}} \times 100 $ So the gain percentage = $ \dfrac{{405 - 300}}{{300}} \times 100 $ So the gain percentage = $ \dfrac{{105}}{{300}} \times 100 = 35 $ %.So he has to sell the remaining goods at a gain percentage of 35% so that he gets overall 20% profit on the whole transaction.So this is the required answer.Note: Whenever we face such types of questions the key concept we have to remember is that the gain percentage is the ratio of the difference of the selling and the cost price to the cost price multiplied by 100, so first find out the overall profit such that he gains 20 % on the whole transaction as above so the selling price is the sum of the overall profit and the cost price of the remainder of goods then use the above described formula we will get the required answer. CONCEPT 1: Introduction • This unit would comprise of six main terms at large namely:
• CASE 1: There was a trade fair, in which livestock was being sold. A farmer bought a cow from one trader at Rs. 10000. In this transaction the trader earned a profit of Rs. 2000. So, from this transaction we could easily infer that the trader earned a profit on selling the cow to the farmer, so the cost price for the trader comes out to be Rs. 8000/-. Now consider another case, • CASE 2: The farmer sells the cow to his brother at Rs.12000, now the selling price of the previous transaction become the cost price of this transaction, since the seller and buyer have changed. Now CP here is Rs. 10000. So, what we conclude is that we need to first chalk out the transaction that is being discussed before advancing towards any calculations. Students, we would be analyzing the underlying concepts rather than relying on ready-made formulae, so that we could solve any problem related to this topic, and at the end of all this concept building, you would be in a position to write all the formulas on you own. Just remember basic things like, if SP is greater that means profit is made, and if CP is greater than SP, loss is incurred. Also, profit % or loss % would always be calculated by keeping CP as reference, as evident from the previous statement. • This unit requires just basic arithmetic and knowledge of percentage to cover entire concepts. Let’s take an example and understand all the concepts one by one. • Example 1: A boy sells his bicycle at Rs. 600, and in this situation, he gains 20%. Calculate profit, CP and SP. Solution: Here we have a situation in which a boy is selling his bicycle. We get the selling price that is given in the question itself, i.e., Rs. 600. Now, as stated earlier we need to focus on the transaction involved, upon selling the bicycle at Rs.600, he gains 20%, so we get an idea that the SP is 20% more than the CP. So, we easily calculate CP as Rs. 500, and profit as Rs. 100. Till now, we have not discussed any formulae, rather solely relied on concepts and analysis of transaction involved. • Example 2: Ram purchased a TV at Rs. 12000, and sold it at Rs. 15000, find the loss or profit involved. Solution: Here, we have the purchase price, that is the CP = Rs.12000, also the selling price is 15000, so we see that the SP > CP, therefore we have profit involved here. So, profit would be how higher the SP is than CP, so we get, Profit = SP-CP. So, Profit = 15000-12000= 3000 Now, bonus question, lets calculate profit % here, for that again concepts come into play, since profit is calculate by keeping the CP as the reference, therefore for calculating Profit %, we need to take CP as reference again and calculate that how much % more is SP than CP. Or in more simpler terms, Profit is what % of CP. Task done!!!! So, Profit % = (Profit/CP) x100 OR Profit % = ((SP-CP)/CP) x100. Now, calculate… • Now, coming to the last two topics left, and as the customary approach that we have been following, I would be again telling you a story for perfect visualization. • So, you visit a shopping complex and see your favourite watch out there, now you see the label on it that states Rs. 4000. Now, the salesman approaches you and starts telling you about the functions of it, but what is more important is the discount about which he tells you would be provided, being 25%. You find the deal nice and buy it. Now, from the above case, we deduce that the MP of the watch is Rs.4000, and the discount provided is 25%. Since discount is provided over the MP so, we calculate the value of discount as 25% of MP, i.e., Rs.1000. And we get the SP as MP − Discount = Rs.3000. NOTE: Since discount is provided on MP, therefore for calculating discount, using discount%, we would always use MP as the reference. As was the case with Profit or Loss %, in which we used CP as the reference. Let’s take a quick example to brush up the concepts discussed. • Example 1: The price of one banana is Rs.5, Ram buys two dozen, when told that he would be getting a discount of Rs.6 per dozen of the bananas bought. Find the price Ram needs to pay and the discount % provided. Solution: Here we see that one banana costs Rs.5, so for 24 bananas, Ram needs to pay Rs. 24×5 = Rs.120. But, for each dozen he gets a discount of Rs. 6, so the net discount comes out to be = Rs.12. Therefore, the SP comes out to be Rs. 120-12= Rs.108 (This is the amount Ram need to pay to get 2 dozen of bananas). Now, for discount %, as discussed earlier, we need to consider MP as the reference value for calculating the same. So, discount % = (Discount/MP) x100. Which comes out to be: (12/120) x100 = 10%. • Everything discussed above employs only basic aptitude and the concepts underlying these terms. Having said that, it could be inferred now that we are in a position to work out any problem given to us. • Here are the formulas, just for reference,
PROBLEMS ON PROFIT AND LOSS FOUNDATION
a. 4 % b. 3 % c. 5 % d. 10 % e. None of these
a. 6 % b. 5 % c. 4 % d. 3 % e. None of these
profit? a. Rs. 1380 b. Rs. 1160 c. Rs. 1260 d. Rs. 1400 e. None of these
a. 4 % b. 2 % c. 0.5 % d. 1 % e. None of these
a. 3 b. 4 c. 5 d. 6 e. None of these MODERATE
a. Rs. 350 b. Rs. 500 c. Rs. 650 d. Rs. 800 e. None of these
a. Rs. 400 b. Rs. 500 c. Rs. 700 d. Rs. 750 e. None of these
a. No profit, No loss b. 5 % c. 8 % d. 10 % e. None of these
a. Rs. 72.5 b. Rs. 71 c. Rs. 72 d. Rs. 70 e. None of these
a. Rs. 500 b. Rs. 540 c. Rs. 575 d. Rs. 600 e. None of these HOTS -HIGH ORDER THINKING SKILLS
a. Rs. 80 b. Rs. 75 c. Rs. 90 d. Rs. 100 e. None of these
a. 47% profit b. 51% profit c. 36% loss d. 28% loss e. None of these
a. Rs. 500 profit b. Rs. 1000 loss c. Rs. 1500 profit d. No profit, no loss e. None of these
a. 89% gain b. 120% loss c. 140% loss d. 143.75% gain e. None of these
a. 100% b. 76% c. 54% d. 43% e. None of these SOLUTIONS FOUNDATION CP = Rs. 27.50, SP = Rs. 28.60 Then Gain = SP – CP = 28.60 – 27.50 = Rs. 1.10 Since, Gain % = (gain × 100/CP) % » Gain % = (1.10 × 100/27.50) % = 4% CP = Rs. 490, SP = Rs. 465.50 Loss = CP – SP = 490 – 465.50 = Rs. 24.50 Loss% = (loss × 100/CP) % = (24.50 × 100/490) % = 5% Let the new SP be Rs. X then 100 – loss%/1st SP = 100 + gain%/2nd SP » 100 – 5/1140 = 100 + 5/X » X = 105 × 1140/95 = Rs. 1260 Here, since both gain and loss percent is same, hence the resultant value would be loss percent only. » Loss % = a2/100 [where a = 10 %] = 1 % CP of 6 toffees = Rs. 1, CP of 1 toffee = Rs. 1/6 SP of X toffee = Rs. 1 [where X is no. of toffees to sell] SP of 1 toffee = Rs. 1/X Gain % = 20/100 = {(1/X) – (1/6)}/ (1/6) » 1/5 × 1/6 = 1/X – 1/6 » X = 5 MODERATE 110 % of SP = 616 (Rate of sales tax = 10 %) SP = 616 × 100/110 = Rs. 560 CP = (100 × SP) / (100 + gain %) = (100 × 560) / (100 + 12) = Rs. 500 Let CP be Rs. X then, 900 – X = 2(X – 450) [Profit = 2 Loss] 3X = 1800 X = Rs. 600 CP = Rs. 600, gain required = 25 % SP = (100 + gain %) × CP/100 SP = (100 + 25) × 600/100 = Rs. 750 Total CP of mixture = 26 × 20 + 30 × 36 520 + 1080 = Rs. 1600, SP = 30 × 56 = Rs. 1680 % profit = 80/1600 × 100 = 5 % Price of 14 shirts = 14 × 45 = Rs. 630 25 pants = 25 × 55 = Rs. 1375 Total price of 39 items = Rs. 2005 Price = (2005/39) × 1.40 [Overall profit = 40 %] = 71.97 = Rs. 72 (Approx.) Old Profit % = 15/100 = {(SP)1 – CP}/CP …(i) New Profit % = 20/100 = {(SP)2 – CP}/CP …(ii) [ Here, (SP)2 = Rs. 600] From (ii), we get CP = Rs. 500 Divide (i) and (ii): ¾ = {(SP)1 – 500}/ (600 – 500) Hence, (SP)1 = Former Selling price = Rs. 575 HOTS- HIGH ORDER THINKING SKILLS Let the CP of each pen be Rs. 100 At the profit of 10 %, SP of 40 pens = (100 + 10) × 40 = Rs. 4400 At the profit of 20 %, SP of 50 pens = (100 +20) × 50 = Rs. 6000 SP of 90 pens = Rs. (4400 + 6000) = Rs. 10400 CP of 90 pens = Rs. (90 × 100) = Rs. 9000 At the profit of 15 %, SP of 90 pens = Rs. (90 × 115) = Rs. 10350 Difference in SP = Rs. (10400 – 10350) = Rs. 50 If the difference is Rs. 50, then CP = Rs. 100 If the difference is Rs. 40, then CP = (100 × 40) / 50 = Rs. 80 Hence, the cost price of each pen is Rs. 80 Total CP of articles = 750 × 0.6 = Rs. 450 [CP of 1 article = Rs. 0.6] By selling 600 articles, Sarika should make a 40 % profit on the outlay. This means that the selling price for 600 articles should be 1.4 × 450 = Rs. 630 Thus, selling price per article = 630/600 = 63/60 = Rs. 1.05 [ SP of 1 article] Since, Sarika sells only 630 articles at this price, her total recovery = 1.05 × 630 = Rs. 661.5 Hence, actual profit percent = {(661.5 – 450) / 450} × 100 = 47 % Thus, Sarika earns 47 % profit on her total investment. Total number of i-phones = 15 .’. Total number of i-pads = 25-15 = 10 Total CP = Rs. 205000 Since, Kritika sells 80 % of both goods at a profit of Rs. 40000, therefore, cost of 80 % of the goods = 0.8 × 205000 = Rs. 164000 Total amount recovered (or SP) = Rs. (164000 + 40000) = Rs. 204000 Hence, loss = Rs. (205000 – 204000) = Rs. 1000 Hence, Kritika’s overall loss is Rs. 1000 Cost price = Rs. 240000 [Total 3000 copies] Published price = Rs. 325 [Published price] Content Powered by Leap Skills https://www.leapskills.in/ Selling price = (75/100) × 325 = Rs. 243.75 No. of free copies = 500 + (2500/25) = 500 + 100 = 600 So, total selling price = 2400 × 243.75 = Rs. 585000 Hence, percentage gain = {(585000 – 240000) / 240000} × 100 = (345000/240000) × 100 = 143.75 % Hence, the overall gain is 143.75 % Let CP of cab driver be price of petrol = Rs. 30 per litre His, SP would be to carry 3 passengers Let cost of 1 passenger be Rs. X Initially he made profit of 20 % » P% = 20/100 = (SP – CP) / CP » 20/100 = (3x – 30) / 30 » X = Rs. 12 Now, CP of petrol = Rs. 24 per litre SP = 4 (cost of 1 passenger) = Rs. 48 = profit % = {(48 – 24) / 24} × 100 = 100 % |