CP & SP

  Q.1 If selling price of an article is   of its cost price, the percentage profit in the transaction isA)  %B) 98 %C) 33  %D) None of theseAns. C S.P. = 4/3 C.P. Profit = S.P. ??C.P. =   C.P. – C.P. =  %profit =   x 100 = 33 % Q.2 By selling a doll at $342, Mac lost 5%.At what price should he have sold it to gain 5%? A) $378B) $380C) $410D) $462 Ans. A If cost price of the doll is x, 0.95 x = 342? x =   = $360Now to gain 5%, new selling price = 1.05 x 360 = $378Q.3 If a dealer were to diminish the selling price of his wares by 10% he would double his sale making the same profit as before . In what ratio his profit diminsh if he were to increase his selling price by 10% and thereby half his sale A) 20 %  B) 25 % C) 30 % D) 35 % Ans. B Let CP of each article be ‘x’, SP of each article be ‘y’ and nos. of articles sold be ‘z’.therefore, profit = z*(y-x) case 1: Profit (P1) = z*(y-x) = 2z*(0.9y – x)solving for x and y we get:x = 0.8y ……………eq.1 therefore P1 = 0.2yz….eq.2 case 2:Profit P2 =  0.5z*(1.1y – x) ……….eq.3putting eq.1 in eq.3 we get:P2 = 0.15yz therefore ratio of diminishing profit = (P1 – P2)/P1 = 1/4 or 25% 🙂  Ratio of diminishing profit: 1/4. % of diminishing profit = 25% Q.4 How much percent must be added to the cost price of goods so that a profit of 20% must be made after giving a discount of 10% from the market price? A) 33 1/3 B) 32 1/3 C) 33 ½ D) 32 ½ Ans. A Let Mp= 100 RsSp after 10% discount = 100*90/100=90to have profit of 20%.120% CP=selling priceCP=SP/120*100=90/120*100=75RsMP is 25Rs more than Cppercentage added amount =25/75*100=33 1/3% Q.5 A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:A) No profit & No lossB) 5 % C) 8 %D) 10 %Ans. B Explanation:C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.  Gain = 80 x 100 % = 5%.1600        

Q.1 A watch passes through three hands and each gains 25%. If the third sells it for $250, what did the first pay for it (in $)?A) 102B) 117C) 128D) None of theseAns. C If first person paid $x for the watch, S.P. of first person = C.P. of second person = 1.25xS.P. of second person = C.P. of third person = 1.25 × 1.25xS.P. of third person = 1.25 × 1.25 × 1.25x = 250? C.P. of first = = $128 Q.2 A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is how much % A) 5.3 % B) 4.3 % C) 5.1 % D) 4.1 % Ans. A shortcut,Learn this formula: Error/True weight- Error *100Let True weight is 1000 Error=950 (Given)Therefore,1000-950/1000-(1000-950)*100(Error is calculated as = True weight -Error)=5.26 % or 5.3 % Ans. Q.3 A man buys 1000 items at $3 each. He sells 700 of them at $4.50 each, and the rest at $2.50 each. Find his average profit per item sold. A) $0.90 B) $900 C) $1.285 D) $1.50 Ans. A A man buys 1000 items for $3 eachTotal cost or C.P. = 1000 3 = $3000Total selling price of 700 items at 4.50 = 700 4.50 = $3150And selling price of rest of the items i.e. (1000 – 700) at 2.50 = 300 2.50 = 750Total S.P. = 3150 + 750 = 3900Now profit = 3900 – 3000 = 900Average profit = = = $0.90 Q.4 A bought 20 kg of sugar at the rate of Rs. 8.50 per kg and 30 kg of sugar at the rate of 9.75 per kg. He mixed the two. At what price per kg should he sell the mixture to get 25% profit on the cost price? A) Rs.11.50 B) Rs.12.50 C) Rs.10.50 D) Rs.10.00 Ans. AApply direct formula :Selling price of the mixture = {(20 × 8.5 + 30 × 9.75}/50 × 1.25 = 11.56 Q.5 A bought 20 kg of sugar at the rate of Rs. 8.50 per kg and 30 kg of sugar at the rate of 9.75 per kg. He mixed the two. At what price per kg should he sell the mixture to get 25% profit on the cost price?A) Rs.11.50B) Rs.12.50C) Rs.10.50D) Rs.10.00 Ans. A Apply direct formula :Selling price of the mixture = {(20 × 8.5 + 30 × } × 1.25 = 11.56 ??11.50    

Q.1 A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs. 40. What is the reduced price per dozen ? A) Rs. 3 B) Rs. 5 C) Rs. 8 D) Rs . 9 Ans. A He purchases 64 more bananas for 40% of Rs. 40 or Rs. 16 Therefore, reduced price per dozen = 16/64 * 12 = Rs. 3Q.2 A man buys 5 horses & 10 cows for Rs. 1600. He sells horses at a profit of 15% & cows at loss of 10%. If his overall profit was Rs.90,what was the cost price of horse & cow ? A) 100 B) 200 C) 300 D) 400 Ans. B Let x be cost price of horse & y be the cost price of cowTherefore, C.P. of 5 horses = Rs.5xC.P. of 10 cows = Rs. 10yThus, 5x+10y = 1600 —-1Since Profit is 15% on the horsesTherefore, Profit on the sale of Rs.5x = 15*5x/100 = 3x/4Similarly, Loss on the cows is 10 % Thus, Loss on the sale of Rs. 10y = 10y*10/100=yAgain,Profit on horses – Loss on cows = Rs. 903/4x – y = 903x-4y = 360—-2Thus on solving these two equations, we getX = Rs. 200 Q.3 A man brought a merchandise whose price was listed at Rs. 160. He was given successive discounts of 20% & 10%. What price he paid for the merchandise ? A) 115.20 B) 116.0 C) 115.0 D) 116.20 Ans. A Since he was given at first discount of 20%100-20 = 80 Therefore, If Rs. 100 is listed price, then S.P. = Rs. 80 & If Rs. 160 is listed price then S.P. = 80/100*160 = Rs.128 He was again given a discount of 10%100 – 10 = 90 If Rs. 100 is the listed price, S.P.is Rs. 90 If Rs. 128 is the listed price, S.P. is Rs.90/100 *128= 115.20 Q.4 A dealer allows 10% discount on the list price of a certain article & yet makes a profit of Rs.25% on each article. Find the cost price of the article when the list price is Rs. 50. A) 34 B) 35 C) 36 D) 37 Ans. C Let C.P. of the article be Rs. 100Then for 25% profit S.P. = Rs.125—-iIf list price is Rs.100, S.P. = Rs. 90—-iiIf S.P. is Rs. 90, List Price = Rs. 100 If S.P. is Rs. 125, List Price = 100/90*125 = 1250/9 If list price is Rs. 1250/9, then C.P. = Rs.100 If list Price is Rs. 50, then C.P.= 100*50*9 / 1250 = Rs. 36 Q.5 A carpenter undertakes to supply 2000 tables at Rs. 17.25 each. He estimates that if 10% are defective which will be sold at 50%, then the profit will be 15% on his whole outlay. When the tables were supplied 70% of the tables were found defective. What loss did the carpenter incur ?A) Rs. 6075B) Rs. 7800C) Rs. 16075D) Rs. 4666Ans. A10% of 2000= 200S.P. of 200 tables at 50 % = Rs. 200*17.25/2= Rs. 1725S.P. of remaining 1800 tables=Rs. 1800 * 17.25= Rs. 31050Rs. 31050+1725= Rs. 32775Now, Rs. 32775 includes 15 % profitTherefore, C.P.= 100 / 115*32775 =Rs. 28500Now, the actual S.P.=2000*30/115*17.25+2000*70/100*17.25/2= 2000* (30/100 + 35/100) * 17.25=20*65*17.25= Rs. 22425Therefore, Loss = C.P. – S.P. = 28500 – 22425= 6075    

Q.1 The C.P. of 6 tables is equal to the S.P. of 4 tables . What is the Profit % A) 47 % B) 48 % C) 49 % D) 50 % Ans. D Shortcut: x-y/y * 100 or 6-4/4 * 100 = 2/4*100 = 50% Q.2 A machine is sold for Rs. 5060 at a gain of 10 %. What would have been the gain or loss % if it had been sold for Rs. 4370 ? A) 5 % B) 6 % C) 7 % D) 8 % Ans. A Shortcut : C.P. = 100/110 * 5060 = Rs. 4600 In this case there is always loss % Loss% = C.P – S.P. / C.P. * 100 Or 5% Q.3 Mohan sold a book at a profit of 6%. Had he sold it for Rs. 2 more he would have gained 10% C.P. of books ? A) 50 B) 51 C) 52 D) 53 Ans. A Q.4 A man sold two houses for Rs. 800000 on one he gains 20 % while on the other he losses 20%. How much does he gain or loss in the whole transaction ? A) 4 % B) 5% C) 6 % D) 7 % Ans. A Shortcut: (20/10)2 = 4 % Q.5 A shopkeeper marks his goods at 20% above his cost price & allows purchases a discount of 10 % for cash . What profit % does he make ? A) 6 % B) 7 % C) 8 % D) 9 % Ans. C Shortcut: x-y-xy/100 % 20-10-200/100 =8 %      

Q.1 Person purchases 100pens at a discount of 10%. Then net amount of money spent by the person to purchase the pens is Rs.600. The selling expenses incurred by the person are 15% on the net cost price. What would be the S.P. for 100 pens in order to earn a profit of 25% ?A) Rs. 875B) Rs. 811C) Rs. 862.50D) Rs. 802.50Ans. CTotal cost price = 600+15% of 600=600 + 600 * 15/100Rs. 690Profit = 25%Thus, S.P.=C.P. [100+profit / 100]Or 690[100+25 / 100] 690*125/100 = Rs.862.50 Q.2 Left pan of a faulty weighs 100 gms more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1kg weight measure. If he sells his goods at the listed cost price, what is his gain % ?A) 200/9 %B) 100/11 %C) 200/11 %D) 1000/9 %Ans. CLet purchased amount be 1100 g & the cost price of 1100 g be Rs. xTherefore, he pays for 1000 g & buys 1100gCost Price of 1000g = Rs.10/11xTherefore, net profit = Rs.x/11Similarly while selling if he sells 1000g. He would actually be selling 900kg at the price of 1000kgSimilarly, once again the profit would be Rs. x/11Therefore total profit = Rs.2x/11 * 100In terms of percentage ,this would be 200/11% Q.3 A man purchase 8 pens for Rs. 9 & sells 9 pens for Rs.8. How much Profit or Loss % ? A) 20.98 % B) -20.98% C) 19.98 % D) 19.98 % Ans. B Shortcut: 8 9 9 8 = 64-81 / 81 = -20.98 % Since it is in negative that’s why it is Loss % Q.4 A dishonest dealer uses a weight of 950 gm for 1 kg gain % ? A) 5.26 % B) 6.26 % C) 5.30 % D) 6.30 % Ans. A Shortcut: Error / true value * 100 = 1000-950 / 1000-(1000-950) * 100 50/950 * 100 = 5.26 % Q.5 A shopkeeper sells his product at a profit of 10 % & uses a weight which is 20 % less. What is the total gain % ? A) 39.7 % B) 37.5 % C) 40.20 % D) 36.2 % Ans. B Shortcut : Gain % + % less in weight / 100 – % less in weight * 100 10+20/100-20 * 100 30/80*100 = 37.5 %    

Q.1 One typewriter marked for sale at Rs. 480. A dealer allows a discount of 10% & yet makes profit of 8%. What should his gain if no discount were allowed ?A) Rs. 38B) Rs. 48C) Rs. 20D) Rs. 80Ans. DLet C.P. of typewriter is Rs.= 100Profit = 8 %Therefore, S.P. = Rs. 108Since discount = 10%Hence if Rs. 100 is the marked price , then S.P.= Rs. 90If Rs. 90 is S.P. then marked price = Rs. 100Therefore, If Rs. 108 is S.P., then marked price = 100 * 108 / 90= Rs. 120If Rs. 120 is the marked price & no discount is allowed then Profit = Rs. 20 (Since 120-100=20)If Rs. 480 is the marked price then profit = 20 * 480 / 120 = Rs. 80 Q.2 Mohan sells two horses for Rs. 1955 each. On one of them he gains 15 % & on the other he losses 15 %. Find the total gain or loss ?A) Loss of Rs. 90B) Gain of Rs. 90C) Profit of Rs. 150D) No loss & no profitAns. AProfit on one horse = 15 %If S.P, is Rs.115, then C.P. = Rs.100Hence if S.P. is Rs.1955, then C.P.= 100 * 1955 / 115= Rs. 1700On the other horse, since loss = 15 %Hence if S.P. is Rs.85, then C.P. = Rs. 100Hence if S.P. is Rs. 1955, then C.P. = 100 * 1955 / 85Rs. 2300Therefore, C.P. of both the horses = 1700 + 2300= Rs.4000& S.P. of both the horses = 1955 + 1955 = 3910Thus, actual loss on both the horses = 4000 – 3910 = Rs. 90 Q.3 A dishonest shopkeeper deceives by 15% at the time of purchase of the article & also 15 % at the time of sale . Find out the % of profit ?A) 15%B) 32 ½ %C) 33 %D) 30 %Ans. BLet he purchase goods of Rs. 100If Rs. 100 goods is sold in Rs. 115Therefore, 115 goods is sold in Rs. 115 * 115 / 100 = 23 * 23 / 4= 132Hence profit = 132 ¼ – 100= 32 ¼ % Q.4 A person purchases 90 clocks & sells 40 clocks at a gain of 10% & 50 clocks at a gain of 20%. Had he sold all of them at a uniform profit of 15 % he would have got Rs. 40 less. Find the cost price of each clock ?A) Rs. 70B) Rs. 80C) Rs. 90D) Rs. 100Ans. BLet C.P. of clock be Rs.100 eachBy profit of 10% S.P. of 40 clocks = 110*40 = Rs. 4400By profit of 20% S.P. of 50 clocks = 120 *50 = Rs. 6000Total S.P. = Rs. 4400 + 6000= Rs. 10400C.P. of 90 clocks = 90 * 100 = Rs.9000By profit of 15% S.P. of 90 clocks = 90 * 115 = Rs. 10350Difference = 10400 – 10350=Rs. 50If the difference is Rs. 50, then C.P. = Rs. 100If the difference is Rs. 40 then C.P. = 100 * 40 / 50=Rs. 80 Q.5 A trader sold 20 p.c of his stock at 10 p.c profit & 50 p.c of the remainder of his stock at 10 p.c. loss. What would be the rate of profit for sale of the remainder of his stock in order that the trader may make an overall profit of 5 p.c. over his entire stock ?A) 17.5%B) 17.2%C) 18.5%D) 18.2%Ans. ALet C.P. of entire stock is Rs.100Therefore C.P. of 20% stock = 100 * 20 / 100 =Rs. 20This stock is sold at 10% profit .S.P. of this part of stock = 110 * 50 / 100 =Rs. 22Now,50 % of this remainder = 80 * 50 / 100= 40% of the entire stockC.P. of this part of stock =Rs.40S.P. of this part of stock =Rs.90 * 40 / 100 =Rs. 36& S.P. of the entire stock at 5% profit= 105 * 100 / 100 =Rs. 105Therefore, S.P. of remainder = 105 – (22+36) = Rs. 47& C.P. of the remainder = 100-20-40=Rs.40Therefore, rate of profit of the remainder = (47-40) * 100 / 40=17 * 100 / 40 = 17.5% Ans.