Profit And Loss — Part 2 MCQs with Explanations

100 --- 10%↓(1 st discount) → 90 --- 5%↓ → 85.5 Net discount = 100 - 85.5 = 14.5%

% Profit = $$\frac{{25}}{{100}}$$ = $$\frac{{120 + {\text{k}}}}{{880}}$$ → k = 100 Thus, Net % profit = $$\frac{{100 \times 100}}{{1000}}$$ = 10%

100 (Initial CP) --- 20%↑ (initial profit) → 120(SP) 120 (SP) --- 25%↑ → 150 (New SP) Let x be the new Cost price Selling Price = 150 x × 1.25 = 150 x = 120 % change = $$ {\frac{{120 - 100}}{{100}}} \times 100$$ = 20%

120 (CP) --- 15% ↓(loss) → 102 (SP) Mental work: 10% of Rs. 120 = 12 5% of Rs 120 = 6

Set up cost = Rs. 2800 Paper etc = Rs. 1600 Printing cost = Rs. 3200 Total cost = Rs. 7600 Total sale price = 1500 × 5 = 7500 Let amount obtained from advertising be x then, (7500 + x) - 7600 = 25% of 7500 x = 1975

Suppose he buy 1 quintal of Rice in Rs.150. 10% is spoiled so he now have to sell of 90 kg remaining). But he has to make a profit of 20%,so he will sell 90kg for Rs. 180 This means his selling price is Rs. 200 per quintal.

Selling price mix EP, = (CP + 9.09% of CP) 48 = $$\frac{{12}}{{11}}$$ of CP CP = 44 No, using Alligation method, 4 : 1 Thus, X = 44 Thus, the price of speed brand is Rs. 28/litre.

Let the marked price be 100 100 == 20% ↓(discount) ⇒ 80 == 10%↓ (discount) ⇒ 72(CP) == 10%↑ (interior) ⇒ 79.2(Total CP) Now, selling price would be 25% above the Total cost price. SP = 79.2 + 25% of 79.2 SP = 99 Now, On comparing, 100 ⇒ 800000 99 ⇒ $$\frac{{800000}}{{100}} \times 99$$ ⇒ 7,92,000 So, SP = Rs. 7,92,000

Ratio of selling price and Cost Price, SP : CP = 12 : 9 =4 : 3 Profit of 3 oranges = Rs. 1 (Let CP = Rs. 1) Profit = $$\frac{1}{3}$$ = 33.33% and, Discount = 11.11% Since, CP : SP : MP = 3 : 4 : 4.5 Profit doubles that of discount. So, % point discount = 33.33% - 11.11% = 22.22% point. Detail Explanation: 12 C.P = 9 S.P, So profit % = $$\frac{{12\,{\text{C}}{\text{.P}}{\text{.}} - 9\,{\text{C}}{\text{.P}}{\text{.}}}}{{9\,{\text{C}}{\text{.P}}{\text{.}}}}$$ = 33.33. Then it is said that, 5 SP - 5 CP = 10 MP -10 SP From that we get relation between MP and SP, that is, 27 SP = 24 MP(With help of 12 CP = 9 SP) THEN DISCOUNT % = $$\frac{{{\text{MP}} - {\text{SP}}}}{{{\text{MP}}}}$$ = 11.11% So, % point discount = 33.33% - 11.11% = 22.22%

Candle - - - - - - - - Bulb CP . . . . A - - - - - - - - B SP . . . . C - - - - - - - - D $$\eqalign{ & and.\,C = 2A \cr & {\text{Profit}} = 10\left( {B - A} \right) = 3D \cr & {\text{Loss}} = 10\left( {C - D} \right) = 4B \cr & {\text{Profit}}\% = \frac{{ {3D \times 100} }}{{10A}} \cr & {\text{Loss}}\% = \frac{{ {4B \times 100} }}{{10C}} \cr & {\text{Now,}}\,{\text{By}}\,{\text{the}}\,{\text{questions}}, \cr & \frac{{ {3D \times 100} }}{{10A}} = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{B}{D} = \frac{3}{2} = 3:2 \cr} $$

$$\eqalign{ & {\text{CP of one egg in }}{{\text{1}}^{st}}{\text{ case}} \cr & = \frac{1}{3} = 33.33\,{\text{paise}} \cr & {\text{CP of one egg in}}\,{2^{nd}}{\text{ case}} \cr & = \frac{1}{6} = 16.66\,{\text{paise}} \cr & {\text{Average}}\,{\text{CP}} \cr & = \frac{{ {33.33 + 16.66} }}{2} \cr & = 25\,{\text{paise}} \cr & {\text{Selling}}\,{\text{price}}\,{\text{of}}\,{\text{9}}\,{\text{eggs}} \cr & = Rs.\,2 \cr & {\text{SP}}\,{\text{of}}\,{\text{one}}\,{\text{egg}} \cr & = \frac{{200}}{9} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = \frac{{ {\left( {25 - {\frac{{200}}{9}} } \right) \times 100} }}{{25}} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = 11.11\,({\text{loss}}) \cr} $$

Let CP's be Rs. 1000 each, their respective SP will be, 1000 == 25%↑ ⇒ 1250 [person calculating profit on the CP] 1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on SP: 25% of SP = 33.33% of CP] The difference turned out to be = 83.33. This has occured when we have assumed the CP as 1000. But, we are given difference of Rs. 100 So, on comparing, 83.33 = 1000 1 = $$\frac{{1000}}{{83.33}}$$ 100 = $$\frac{{1000}}{{83.33}} \times 100$$ = Rs. 1200

For 20% profit on selling price means $$\frac{1}{5}$$ of 3000 i.e. Rs. 600 Now, let the CP = Rs. 100, Then, SP with 20% profit = Rs. 120 For 20% profit on selling price means cost is 100 + profit is 20 = selling price is 120. Means selling price is 120% of cost price. Now selling price is 120% ie 3000 then find 100% amount which will be cost. Cost = $$\frac{{3000}}{{120}}\% $$ = $$\frac{{3000}}{{\frac{6}{5}}}$$ Because, 120% = $$\frac{6}{5}$$ = 3000 x $$\frac{5}{6}$$ = 2500 Cost is 2500 Thus profit is 20% i.e. $$\frac{1}{5}$$ x 2500 = 500Thus, Difference is 600 - 500 = Rs.100

Total sales revenue (Old) = 2000 × 3.25 × 0.75 = 4875 [0.75 as 25% discount was allowed] Profit old = Total sales revenue - 4800 = 4875 - 4800 = 75 Total sales revenue (New) = 3000 × 4.25 × 0.75 = 9562.5 [New price is calculated on doctors samples as well.] Profit new = 9562.5 - 4800 = 4762.5 Ratio, $$\frac{{{\text{Profi}}{{\text{t}}_{{\text{new}}}}}}{{{\text{Profi}}{{\text{t}}_{{\text{old}}}}}} = \frac{{4762.5}}{{75}} = 63.5$$

The successive discounts must have been of 10% each As 20 (CP) == 25%↑ ⇒ 25(MP) == 10↓ ⇒ 22.5 == 10%↓ ⇒ 20.25(SP) Profit = 20.25 - 20 = 0.25 Increased percentage if price have been increased twice successively instead of reducing it, 20(MP) == 10%↑ ⇒ 27.5 == 10%↑ ⇒ 30.25 Profit = 30.25 - 20 = 10.25. Profit Change = 10.25 - 0.25 = 10 Percentage Profit change, = $$\frac{{10 \times 100}}{{0.25}}$$ = 4000%

The company is able to deliver 90% of the manufactured pens. Means to produce 7200 pens they must have to produce 8000 pens as 10% are defectives. So, let K be the manufacturing price of each pen. Total income (including 25% profit) = 8000 × K × 1.25 This same income is obtained by selling 90% manufactured pens at Rs. 10 which is equal to 7200 × 10 Thus, 8000 × K × 1.25 = 7200 × 10 K = Rs. 7.2 [90% of 8000 = 7200]

$$\eqalign{ & {\text{Charge per call in February}} \cr & = \frac{{350}}{{150}} = \frac{7}{3} = 2.33 \cr & {\text{Charge per call in March}} \cr & = \frac{{ {350 + \left( {50 \times 1.4} \right)} }}{{250}} \cr & = \frac{{420}}{{250}} = \frac{{42}}{{25}} = 1.68 \cr & \% {\text{ Cheaper call rate in March}}. \cr & = {\frac{{ {2.33 - 1.68} }}{{2.33}}} \times 100 \cr & = 28\% \cr} $$

$$\eqalign{ & {\text{MP}} = M \cr & {\text{SP}} = \frac{M}{2} \cr & \% \,{\text{Discount}} \cr & = {\frac{{ {\frac{M}{2}} }}{M}} \times 100 \cr & = 50\% \cr} $$

$$\eqalign{ & {\text{CP}} = 500 \cr & {\text{SP}} = 576 \cr & {\text{MP}} = 900\left[ {80\% \,{\text{above}}\,{\text{the}}\,{\text{CP}}} \right] \cr & {\text{Now}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & \left[ {{\text{R = Rate}}\,{\text{of}}\,{\text{Discount}}} \right] \cr & 576 = 900 \times {\left[ {1 - {\frac{R}{{100}}} } \right]^2} \cr & R = 20\% \cr & \cr & {\text{Again}}, \cr & {\text{SP}} = {\text{MP}} \times {\left[ {1 + {\frac{R}{{100}}} } \right]^2} \cr & {\text{SP}} = 900 \times {\left[ {1 + {\frac{{20}}{{100}}} } \right]^2} \cr & {\text{SP}} = 1296 \cr & {\text{New}}\,{\text{Profit}}\,{\text{Percentage}}, \cr & = {\frac{{ {SP - CP} }}{{CP}}} \times 100 \cr & = {\frac{{ {1296 - 500} }}{{500}}} \times 100 \cr & = 159.2\% \cr} $$

CP = $$\frac{{100}}{{120}} = \frac{{10}}{{12}}$$ [Since, he purchases 120 g and pays Rs. 100, by assumption actual CP of 1 g = Re. 1] SP = $$\frac{{135}}{{90}} = \frac{3}{2} = \frac{{18}}{{15}}$$ [Since, Actual MP = 180 as he mark up 80% above, SP = 135, with 25% discount and he sells 90 g instead of 100g] Percentage Profit = $$ {\frac{{\frac{{18}}{{12}} - \frac{{10}}{{12}}}}{{\frac{{10}}{{12}}}}} \times 100 = 80\% $$

Ratio of CP given as 1 : 2 : 4 Let cost of, A = x B = 2x C = 4x Ratio of Number of sell is given as 2 : 5 : 2 Let number of items sold be, A = 2y B = 5y C = 2y Total cost (A + B + C), = (2xy + 10xy + 8xy) = 20xy Profit of A = 0.2xy Profit of B = 2xy Profit of C = 2xy Total profit = 4.2xy % Profit = $$\frac{{4.2{\text{xy}} \times 100}}{{20{\text{xy}}}} = 21\% $$

Primary Cost: 35% of 12600 = 4410 Miscellaneous costs: 2% of 12600 = 252 Gross Profit = 12600 - 4410 - 1400 - 650 - 252 = 5888 Trading Cost = 0.25 × 5888 = 1472 Hence, Net Profit = 4416 % Profit =$$\frac{{4416}}{{14000}} \times100$$ = 31.54% ≈ 31%

While purchasing he would take 1200 grams for the price of 1000 grams. While selling he would sell 900 grams for the price of 1000 grams. Since, CP = SP The profit earned by him, $$\frac{{{\text{Goods Left}}}}{{{\text{Goods Sold}}}} = \frac{{300 \times 100}}{{900}} = $$ $$33.33\% $$

David (100) == 20% ↓(loss) ⇒ Goliath (80) == 25% ↑(gain) ⇒ Hercules(100) == 10% ↓ (loss) ⇒ Goliath (90) Hercules loss corresponds to 10 when David buys the laptop for Rs. 100. Thus, Hercules loss would be Rs. 17,500 when David buys the laptop for 1,75,000.

100 == 10%↓ (1st disc.) ⇒ 90 == 10%↓ ⇒ 81 == 10%↓ ⇒ 72.9 == 10%↓ ⇒ 60(After 5 th discount.) Alternatively , Amount paid in 1 st service = 100 (Assume) Amount paid in 2 nd service = 90 Amount paid in 3 rd service = 81 Amount paid in 4 th service = 72.9 Amount paid in 5 th service = 60 Total amount paid, = (100 +90 +81 +72.9 +60) = 403.9 Total Discount = 500 - 403.9 = 96.1 % Discount = $$\frac{{96.1 \times 100}}{{500}}$$ = 19.42%

Go through the option: 100 (CP) == 80%↑ ⇒ 180(SP) $$\frac{1}{3}$$ of SP = $$\frac{180}{3}$$ = 60 Loss = 40% = 100 - 60 = 40 Hence, option (C) is correct as it gives 40% loss on CP on reducing the price to $$\frac{1}{3}$$ of CP.

CP for one toffee = $$\frac{{100}}{6}$$ SP will be 20% above the CP. So, SP for one toffee = $$\frac{{100}}{6} \times 1.2 = \frac{{100}}{5} = 20$$ Thus, He should sell 5 toffee for Rs. 1 (100 paise)

Let CP of each article be Rs. 29 and SP of each article be Rs. 19 Loss Percentage $$\eqalign{ & = \frac{{ {\left( {29x - 19x} \right) \times 100} }}{{29x}} \cr & = 34.48\% \cr} $$

He gets 14% of loss that means he gets 86% of CP. Thus, Let the CP be Rs. 100 60% of 100 + 16.66% of 60% of 100 + 40% of 100 - x% of 40% of 100 = 86% of 100 70 + 40X = 86 40X = 86 - 70 = 16 X = $$\frac{{16}}{{40}}$$ X = 0.4 Hence, Loss = 1 - 0.4 = 0.6 = 60%

It is based on inverse proportion or product constancy concept. Reduction in price 20% amount of sugar will increase 25% It means, 25% = 6 Kg. So, Initially, total Sugar = 6 × 4 = 24Kg. Thus, Original price of the sugar was, $$\frac{{240}}{{24}}$$ = Rs. 10 per kg. Note: Let initial price of 100 kg Sugar was Rs. 100. Now, 20% decrease in rate then rate of 100 kg sugar would be Rs. 80. So, Rs. 80 = 100 kg sugar. Rs. 1 = $$\frac{{100}}{{80}}$$ kg sugar. Rs. 100 = $$\frac{{100 \times 100}}{{80}}$$ = 125 Kg sugar. Increment in sugar = 25 kg. % increment = $$\frac{{25 \times 100}}{{100}}$$ = 25%. Means 20% rate decrease, 25% of consumption increase.

Let actual cost price of an article be Rs. 1 (in place of X). Now he purchases goods worth Rs. 120 and pays Rs. 80, since 20% discount is allowed. So, the CP = $$\frac{{80}}{{120}} = \frac{2}{3}$$ Again, MP, SP = 135 (since 25% discount) Thus, the trader sells goods worth Rs. 90 instead of 100g and charges Rs. 135. Therefore the effective SP = $$\frac{{135}}{{90}} = \frac{3}{2}$$ $$\eqalign{ & {\text{Profit}}\,\% \cr & = {\frac{{ { {\frac{3}{2}} - {\frac{2}{3}} } }}{{\frac{2}{3}}}} \times 100 \cr & = 125\% \cr} $$

Maintenance, = Rs. (100 × 5 × 30) + (75 × 10 × 30) + (40 × 18 × 30) = 15,000 + 22,500 + 21,600 = Rs. 59,100 Total cost = 2,09,100 Amount Received, = (9 × 250 × 30) + (7 × 400 × 30) + (2 × 600 × 30) = 67,500 + 84,000 + 36,000 = 1, 87, 500 Loss (%), $$\eqalign{ & = {\frac{{209100 - 187500}}{{209100}}} \times 100 \cr & = {\frac{{21600}}{{209100}}} \times 100 \cr & = 10.33\% \cr} $$

Cost price of each book, = $$\frac{{3200}}{{40}}$$ = Rs. 80. Now, Selling Price of 40 books = CP of 40 books + SP of 8 books. Selling Price of 40 books - SP of 8 books = CP of 40 books. SP of 32 books = Rs. 3200 SP of 1 book = $$\frac{{3200}}{{32}}$$ = Rs. 100. So, Selling price of one dozen (12) book = 12 × 100 = Rs. 1200

Let CP = Rs. 100, then SP will be 120. He gives cloth worth Rs. 80 instead of Rs. 100. Hence, % Profit = $$ {\frac{{120 - 80}}{{80}}} \times 100 = 50\% $$

10% of x = 15 % of y, where x + y = 30000 $$\frac{{\text{x}}}{{\text{y}}} = \frac{{3{\text{k}}}}{{2{\text{k}}}}$$ Hence, difference = k = Rs. 6000

40% discount on 500 = $$\frac{{40 \times 500}}{{100}}$$ = Rs. 200 Two successive discount 30% and 10% on 500 would be 500 ===30% discount ⇒ Rs. 350 350 ===10% discount = 315 Total discount in first case = Rs. 200 Total discount in second case = 500 - 315 = Rs. 185 So, difference = Rs. 15

To gain 20% on whole he must sell all good for, Rs. 400 + 20% of 400 = 480 As he get 5% gain on half of the goods i.e. 200 + 5% of 200 = 210 So required balance = 480 - 210 = 270 He must gain Rs. 70 on rest Rs. 200 % gain on remainder goods = $$\frac{{70 \times 100}}{{200}}$$ = 35%

40% discount on 500 = $$\frac{{40 \times 500}}{{100}}$$ = Rs. 200 Two successive discount on 500, = 30% of 500 + 10% of (500 - 30% of 500) = 150 + 10% of 350 = 150 + 35 = Rs. 185 Difference in Discount = 200 - 185 = Rs. 15

$$\eqalign{ & {\text{Gain}}\% \cr & = {\frac{{ {{\text{True}}\,{\text{Weight}} - {\text{False}}\,{\text{Weight}}} }}{{{\text{False}}\,{\text{Weight}}}}} \times 100 \cr & \frac{{100}}{9} = {\frac{{ {1 - x} }}{x}} \times 100 \cr & \frac{{ {1 - x} }}{x} = \frac{1}{9} \cr & 10x = 9 \cr & x = 0.9\,kg = 900\,gms \cr} $$

40% discount on 500 = 200 Two consecutive discount on 500: 500 == 30% down ⇒ 350 == 10% down ⇒ 315 Total discount = 150 + 35 = 185 So, difference = 200 - 185 = Rs. 15