Profit And Loss — Part 1 MCQs with Explanations

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{CP}}\,{\text{be}}\,100 \cr & {\text{Hence}}, \cr & {\text{SP}} = 100 + 12\% \,of\,100 \cr & \,\,\,\,\,\,\, = 112 \cr & {\text{If}}\,{\text{the}}\,{\text{marked}}\,{\text{price}}\,{\text{be}}\,X,\,{\text{then}} \cr & 90\% \,of\,X = 112 \cr & \Rightarrow x = \frac{{ {112 \times 100} }}{{90}} \cr & \Rightarrow x = Rs.\,\frac{{1120}}{9} \cr & {\text{Hence}}, \cr & {\text{Required}}\,{\text{ratio}} \cr & = 100:\,\frac{{1120}}{9} \cr & = 900:1120 \cr & = 45:56 \cr} $$

Let Cost Price was X. X + 14% of X = 2850 X + $$\frac{{14{\text{X}}}}{{100}}$$ = 2850 X + 0.14X = 2850 1.14X = 2850 X = 2500. So, Cost Price = Rs. 2500. Now, Selling Price When profit remains at 8%, = 2500 + 8% of 2500 = Rs. 2700. Short-Cut CP of bicycle = $$\frac{{100}}{{114}}$$ × 2850 = Rs. 2500 SP for a profit of 8% = $$\frac{{108}}{{100}}$$ × 2500 = Rs. 2700

First Method Let CP was 100 for A originally A sells article to B at 10% profit, CP for B = 100 + 10% of 100 = 110 Now, B sells it A again with loss 10% Now, CP for A this time = 110 - 10% of 110 = 99 A makes Profit = 110 - 99 = 11 %profit for A = $$\frac{{11 \times 100}}{{100}}$$ = 11% Second Method It could be easily shown by net percentage change graphic. 100(A) == 10%(Profit) ⇒110(B) == 10%(Loss) ⇒ 99(A) In this transaction A makes a profit of (110 - 99 = 11%) 11% [10% on selling to B and 1% profit on buying back from B]

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{CP}} = {\text{Rs}}.\,X \cr & {\text{Hence}}, \cr & {\text{SP}} = X + 15\% \,{\text{of}}\,X \cr & \,\,\,\,\,\,\,\,\, = \frac{{115X}}{{100}} \cr & \,\,\,\,\,\,\,\,\, = Rs.\,\frac{{23x}}{{20}} \cr & {\text{New}}\,{\text{CP}} = x - 25\% \,{\text{of}}\,X \cr & = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{New}}\,{\text{SP}} = \frac{{3x}}{4} + 32\% \,{\text{of}}\,\frac{{3x}}{4} \cr & = Rs.\,\frac{{99x}}{{100}} \cr & \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question,}} \cr & {\frac{{23x}}{{20}}} - {\frac{{99x}}{{100}}} = 600 \cr & {\text{Or}},\,\frac{{ {115x - 99x} }}{{100}} = 600 \cr & 16x = 600 \times 100 \cr & X = 600 \times \frac{{100}}{{16}} \cr & \,\,\,\,\,\, = Rs.\,3750 \cr} $$

Let the Cost price of the Chair is X. SP = X - 25% of X 720 = 0.75X X = 960 CP = Rs. 960 So, To gain 25%, SP would be = 960 + 25% of 960 =Rs. 1200 Short-cut CP of chair = $$\frac{{100}}{{75}}$$ × 720 = Rs. 960 To gain 25%, SP = $$\frac{{125}}{{100}}$$ × 960 = Rs. 1200

In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut: Loss on total deal, $$\eqalign{ & = {\left( {\frac{{{\text{Common loss or gain percentage}}}}{{10}}} \right)^2} \cr & = {\left( {\frac{{20}}{{10}}} \right)^2} \cr & = 4\% \cr} $$ Alternatively , It can be also calculated through Graphic Change Method: This can be given by, 100 == 20% gain ⇒ 120 == 20% loss ⇒ 96 Loss = 4% (As 100 became 96)

Let the cost price be Rs. 100 then the mark up price which is 30% above the cost price, Mark price = (100 + 30% of 100) = Rs. 130 Shopkeeper gives a discount of 10% on mark up price, then the Selling Price = (130 - 10% of 130) = Rs. 117 Gain = 117 - 100 = Rs. 17 $$\% {\text{gain}} = \frac{{17 \times 100}}{{100}} = 17\% $$ Short Cut method: 100(CP) == 30%↑ ⇒ 130(MP) == 10%↓ ⇒ 117(SP) Gain = 17%

SP = Rs. 39 CP = x(let) Profit % = CP $${\text{or,}}\,\frac{{39 - x}}{x} \times 100 = x$$ $$\left[ {\% \,{\text{profit}} = \frac{{{\text{SP}} - {\text{CP}}}}{{{\text{CP}}}}} \right]$$ $$\eqalign{ & 3900 - 100x = {x^2} \cr & {x^2} + 100 - 3900 = 0 \cr } $$ $$x=30$$ (we cannot take negative value of x)

$$\eqalign{ & {\text{First}}\,{\text{Method}}: \cr & {\text{CP}} = 360000 \cr & {\text{To}}\,{\text{gain}}\,10\% \,{\text{on}}\,{\text{whole}}\,{\text{land}}, \cr & SP = 360000 + 10\% \,\text{of}\,360000 \cr & \,\,\,\,\,\,\,\, = Rs.\,396000 \cr & \frac{1}{3}\,{\text{of}}\,{\text{the}}\,{\text{land}}\,{\text{sold}}\,{\text{on}}\,20\% \,{\text{loss}}. \cr & {\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{land}} \cr & = {\frac{{360000}}{3}} - 20\% \,{\text{of}}\,\, {\frac{{360000}}{3}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}\,{\text{of}}\,{\text{the}}\,{\text{land}} \cr & = \frac{{ {360000 \times 2} }}{5} + 25\% \,{\text{of}}\,\,\frac{{ {360000 \times 2} }}{5} \cr & = Rs.\,180000 \cr & {\text{Thus}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{land}} \cr & = 396000 - 96000 - 180000 \cr & = Rs.\,120000 \cr & \cr & {\text{Second}}\,{\text{Method:}} \cr & {\text{SP of total agricultural }} \cr & {\text{field at a profit of}} \cr & 10\% = \frac{{ {360000 \times 110} )}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\, = Rs.\,396000 \cr & {\text{So,}}\,{\text{SP}}\,{\text{of}}\,\frac{1}{3}\,{\text{of}}\,{\text{field}} \cr & = {\frac{{360000}}{3}} \times {\frac{{80}}{{100}}} \cr & = Rs.\,96000 \cr & {\text{SP}}\,{\text{of}}\,\frac{2}{5}th\,{\text{of}}\,{\text{the}}\,{\text{field}} \cr & = \frac{{ {2 \times 360000 \times 125} }}{{ {5 \times 100} }} \cr & = Rs.\,180000 \cr & {\text{Hence}}, \cr & {\text{SP}}\,{\text{of}}\,{\text{the}}\,{\text{remaining}}\,{\text{field}} \cr & = Rs.\,\left( {396000 - 96000 - 180000} \right) \cr & = Rs.\,120000 \cr} $$

MP = 920 After first discount Marked Price (MP) become, = 920 - 15% of 920 = 782 The Selling Price (SP) = 742.90 Let second discount was x% on 782 782 - x% of 782 = 742.90 $$\frac{{782x}}{{100}}$$ = 39.1 782x = 3910 x = 5% Second Discount = 5% Short-Cut 920 == 15%(1 st discount)) == 782 == x%↓(2 nd discount) ⇒ 742.90 Then, $$\eqalign{ & x\% = \frac{{\left( {782 - 742.90} \right) \times 100}}{{742.90}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{39.1 \times 100}}{{742.90}} \cr & \,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$

Let his CP = Rs. 100. Marked Price = 100 + 25% of 100 = 125. Now, discount = $$\frac{{25}}{2}$$% on MP So, SP = 125 - $$\frac{{25}}{2}$$% of 125 = Rs. 109.375. %Gain = 9.375%. Alternatively use graphic change method: 100(CP) == 25% Up ⇒ 125(MP) == 12.5%down ⇒ 109.375 %Profit = 9.375%

Marked Price = 2000 SP after first Discount of 20% = 2000 - 20% of 2000 = 1600 SP after second Discount of 10% = 1600 - 10% of 1600 = 1440 Now, the final selling price at cash = 1440 - 5% of 1440 = Rs. 1368 Shortcut by using Graphic Change 2000(MP) == 20%(disc.) ⇒ 1600 == 10%(disc.) ⇒ 1440 == 5%(disc.) ⇒ 1368(SP)

Let the price of shirt and trouser be Rs. 100 and Rs. 200 respectively. Then, price of set of shirt and trouser = Rs. 300. After giving 30% discount on the set, Selling Price = 300 - 30% of 300 = 210. Total Discount on Set = 90. And Discount on shirt is 20% alone, SP of shirt alone = 100 - 40% of 100 = 60. Rs. 40 is the discount on shirt then Rs. 50 must be the discount on the trouser. So, discount on trouser = $$\frac{{50 \times 100}}{{200}}$$ = 25%.

Marked Price = 25000. After first discount it become, = 25000 - 20% of 25000 = 20000. After second discount, it becomes = 20000 - 5% of 20000 = 19000. So, SP = 19000. CP for the man who bought it, as he spends 1000 on repair. = 19000 + 1000 = 20000 Profit = 25000 - 20000 = 5000. %Profit = $$\frac{{5000 \times 100}}{{20000}}$$ = 25% Short-Cut 25000(MP) == 20%(Disc.) ⇒ 20000 == 5%(disc.) ⇒19000(CP) Spends on repair = Rs. 1000 Then, CP becomes = 19000 + 1000 = 20000 Profit = 5000 % profit = $$\frac{{5000 \times 100}}{{20000}}$$ = 25%

Let the marked price = Rs. 100 Then, SP = 100 - 20% of 100 = Rs. 80 Profit = 25% Let His CP = X SP = 80 X + 25% of X = 80 Hence, X = Rs. $$\frac{{100 \times 80}}{{125}}$$ = Rs. 64 CP = Rs. 64 Profit after selling on marked price = 100 - 64 = Rs. 36 % gain = $$\frac{{36 \times 100}}{{64}}$$ = 56.25%

Let CP = 100 Then, MP = 100 + 20% of 100 = 120 Now, SP = 120 - 10% of 120 = 108 Gain = 108 - 100 = 8 %Gain = $$\frac{{8 \times 100}}{{100}}$$ = 8% Short-cut 100(CP) == 20%(up) ⇒ 120(MP) == 10%(disc.) ⇒ 108 % gain = 8%

$$\eqalign{ & {\text{Sell}}\,{\text{sugar}} \cr & = 950g\,{\text{instead}}\,{\text{of}}\,1000g \cr & {\text{Profit}}\,{\text{in}}\,{\text{sugar}} \cr & = 1000 - 950 = 50g \cr & {\text{Now}},\,\% \,{\text{profit}} \cr & = \frac{{ {50 \times 100} }}{{950}} = 5 {\frac{5}{{19}}} \% \cr & \cr & {\text{Short - cut}}: \cr & \% \,{\text{profit}} \cr & = {\frac{{{\text{Goods}}\,{\text{lef}}t}}{{{\text{Goods}}\,{\text{sold}}}}} \times 100 \cr & = {\frac{{50}}{{950}}} \times 100 \cr & = 5 {\frac{5}{{19}}} \% \cr} $$

Let the CP be Rs. 100, then SP = 100 + 14.28% of 100 = Rs. 114.28 (As Profit = 14.28%) This profit is arrived after giving discount of 11.11% on the marked price. Let the marked price be x X - 11.11% of X = 114.28 X × $$\frac{{100 - 11.11}}{{100}}$$ = 114.28 X = $$\frac{{114.28 \times 100}}{{8889}}$$ = Rs. 128.56, which is more than 28.56% of CP.

Let the dealer buys 3 kg, 4 kg and 5 kg. Price of total dry fruits = 3 × 100 + 4 × 80 + 5 × 60 = Rs. 920 SP = 920 + 50% of 920 = 1380 Hence, Price of mix dry fruits per kg = $$\frac{{1380}}{{12}}$$ = Rs. 115

Let the marked price = Rs. 100 Then the cost price = 80% of 100 = Rs. 80 After allowing 12% discount on MP, SP become = Rs. 88. % profit = $$\frac{{8 \times 100}}{{80}}$$ = 10%

Discount on one shirt, = 25% of 320 = $$\frac{{320 \times 25}}{{100}}$$ = Rs. 80 Hence, number of shirt he must buy to get a rebate of Rs. 400 = $$\frac{{400}}{{80}}$$ = 5

$$\eqalign{ & {1^{st}}\,{\text{Method}}: \cr & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{prine}}\,{\text{of}}\,{\text{tea}}\,{\text{be}}\,{\text{Rs}}.\,x\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = x - 10\% \,\text{of}\,x = \frac{{9x}}{{10}}\,\text{per kg} \cr & {\text{Now}}, \cr & {\frac{{22500}}{{ {\frac{{9x}}{{10}}} }}} - \frac{{22500}}{x} = 25 \cr & {\text{or}},\,22500\left[ {\frac{{10}}{{9x}} - \frac{1}{x}} \right] = 25 \cr & {\text{or}},\,25 \times 9x = 22500 \cr & {\text{or}},\,x = {\frac{{22500}}{{25\times9}}} = \text{Rs.}\,100 \cr & {\text{Hence,}}\,{\text{new}}\,{\text{price}} \cr & = 90\,{\text{per}}\,{\text{kg}}{\text{}} \cr }$$ $$\eqalign{ & {\text{Thought}}\,{\text{process}}\,{\text{method:}} \cr & {\text{Let the original price be Rs}}{\text{. 100 per kg}}, \cr & {\text{He get tea}} = \frac{{22500}}{{100}} \cr & = 225\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = {\text{ }}90{\text{ per kg}} \cr & {\text{He}}\,{\text{get}}\,{\text{tea}} = \frac{{22500}}{{90}} \cr & = 250\,\text{kg} \cr & {\text{So, reduction price is }}{\text{ Rs. }}90{\text{ per kg}} \cr & {\text{As it enables him to buy 25 kg of more tea}}{\text{.}} \cr} $$

First Method Let Cost Price for A was 100 Then CP for B = 100 + 25% of 100 = 125 CP for C = 125 + 20% of 125 = 150 CP for D = 150 + 10% of 150 = 165 But, D pay Rs. 330, Then it must be equal to 165 = 330 1 = $$\frac{{330}}{{165}}$$ 100 = $$\frac{{330 \times 100}}{{165}} = 200$$ Thus, CP for A = Rs. 200 Short-cut A's CP = $$330 \times \frac{{100}}{{125}} \times \frac{{100}}{{120}} \times \frac{{100}}{{110}}$$ = Rs. 200

In such cases, always loss occurs. It can be calculated by this formula, $$ = \frac{{{{\left( {{\text{loss or gain percentage}}} \right)}^2}}}{{100}} = 4$$ That is 4% of loss Graphic Change method 100 == 20%(loss) ⇒ 120 == 20%(gain) ⇒ 96 % Loss = 4%

CP = Rs. 95. Then SP = 95 + 10% of 95 = Rs. 104.5 Let MP = X. He gives 5% commission on MP. So, SP = X - 5% of X SP = 0.95X 104.5 = 0.95X X = $$\frac{{104.5}}{{0.95}} = 100$$ Thus, MP = Rs. 110 Short-cut 95 == 10%(gain) ⇒ 104.5 == 5%(Commission) ⇒ 109.72 (= 110)

Use Formula, Equivalent Discount = (A + B) - $$\frac{{{\text{AB}}}}{{100}}$$ where A = First Discount, B =Second Discount. Equivalent Discount = (20 + 10) - $$\frac{{20 \times 10}}{{100}}$$ Equivalent Discount = 30 - 2 = 28% Graphic Change Method 100 == 20%(disc.) ⇒ 80 == 10%(disc.) ⇒ 72 Equivalent discount = 28%

Let MP = X CP = 1440 SP = 1440 + 25% of 1440 = Rs. 1800 SP = MP - 25% of MP SP = X - 25% of 100 SP = X - 0.25X 1800 = 0.75X X = 2400 MP = Rs. 2400 Short-Cut Let the marked price = Rs. x Hence, $$\frac{{{\text{75}} \times {\text{x}}}}{{100}} = 1440 \times \frac{{125}}{{100}}$$ ⇒ $$\frac{{1440 \times 125}}{{75}}$$ = Rs. 2400

Equivalent Discount, =(A + B) - $$ {\frac{{{\text{AB}}}}{{100}}} $$ = (10 + 5) - $$ {\frac{{10 \times 5}}{{100}}} $$ = 14.5% Let MP = X Now, X - 14.5% of X = 171(Selling Price) 0.855X = 171 X = 200 Hence, MP = Rs. 200 Going through options, 200(MP) == 10%(disc.) ⇒ 180 == 5%(disc.) ⇒ 171(CP)

To get 20% profit on whole, 1000(CP) ⇒ 20%(gain) ⇒ 1200(SP) Total Profit = 1200 - 1000 = Rs. 200 400 ⇒ 10%(gain) ⇒ 440 He gets Rs. 40 profit on 400 Rest Profit = 200 - 40 = 160 Then he must get Rs. 160 as profit on Rs. 600 Hence, % profit = $$\frac{{160 \times 100}}{{600}}$$ = $$\frac{{80}}{3}$$ = $$26\frac{2}{3}$$%

Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP = X + 20% of X = 1.2x It is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = $$\frac{{16 - 12}}{{16}}$$ = 25%] His selling price = SP - 25% of SP = SP × 0.75 Hence, SP × 0.75 = 1.2X Or, SP = $$\frac{{1.2 \times {\text{x}}}}{{0.75}}$$ = 1.6X This SP is arrived after giving a discount of 20% on MP. Let MP = Y Y - 20% of Y = SP 0.80Y = 1.6X Y = 2X It means that the article has been marked 100% above the cost price. Or Marked Price was twice of cost price.

If the CP of the chair be Rs. x then, Total SP = $$\frac{{{\text{x}} \times 90}}{{100}}$$ + $$\left( {\left( {6000 - {\text{x}}} \right) \times \frac{{110}}{{100}}} \right)$$ Or, 9x + 66000 - 11x = 61000 Or, 2x = 66000 - 61000 = 5000 Or, x = Rs. 2500

He gets 25% profit on the selling price. $$\eqalign{ & Let\,SP = x;\,then \cr & CP = x - {\frac{x}{4}} \cr & = Rs.\,\frac{{3x}}{4} \cr & Hence, \cr & \% \,gain = {\frac{{ {\frac{x}{4}} }}{{ {\frac{{3x}}{4}} }}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3} \cr} $$

100 --- 10%↑ → 110 --- 10%↑ → 121 Equivalent price increase = 21%

Let the CP of 1 kg of sugar be Rs. 100. Then, CP of 900g sugar = $$\frac{{100 \times 900}}{{1000}}$$ = Rs. 90 Hence, profit % = $$ {\frac{{100 - 90}}{{90}}} \times 100$$ = 11.11% If he add 10% impurity then his CP for 1 kg = $$\frac{{100 \times 1000}}{{1100}}$$ = Rs. 90.9 And % profit = $$ {\frac{{100 - 90.9}}{{90.9}}} \times 100$$ = 10.01% If he reduces weight by 5% Then, cost price of 950 g = $$\frac{{100 \times 950}}{{1000}}$$ = Rs 95 and SP = 105; % profit = $$ {\frac{{105 - 95}}{{95}}} \times 100$$ = 10.25%

On an investment of Rs. 4725, a profit of 40% means a profit of 1890. Hence, the targeted sales realization is Rs. 6615. The required equation; 8p + 22 × $$\frac{{3{\text{p}}}}{4}$$ = 6615 Or, 8p + $$\frac{{33{\text{p}}}}{2}$$ = 6615 In the expression for LHS = RHS; we need $$\frac{{33{\text{p}}}}{4}$$ to be odd number. This can only happen when p is not a multiple of 4. Hence, option a and c gets eliminated automatically. Now, we check for option B which is correct.

Assume the cost price = 100 and selling price = 120 Then, when price of petrol is reduced Cost price become 60 and selling price = 160 Profit increased = 100%

He sells only 900 grams when he takes the money for 1 kg. and he sells at a 8% profit (20% markup, 10% discount) Hence, his selling price is Rs. 108 for 900 grams % profit = $$\frac{{18}}{{90}} \times 100$$ = 20%

Total cost = type + Printing + paper, ink = 1000 + 120 × 9 + 540 = 2620 Net sum to be recovered = Rs. 2882 Total magazine sold 784 for = 784 × 2.75 = 2156 Sum obtained from advertisement = 2882 - 2156 = Rs. 726

Let CP = 100; then marked price = 130; Now, revenue $$ = { {\frac{1}{2}} \times 130 + {\frac{1}{4}} \times 0.85 \times 130 + {\frac{1}{4}} \times 0.7 \times 130} $$ $$\eqalign{ & = 65 + 27.65 + 22.5 \cr & = 115.4 \cr & \% {\text{profit}} = \frac{{15.4 \times 100}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15.4\% \cr} $$

While buying, He buys 1100 gram instead of 1000 gram. Suppose he bought 1100 grams for Rs. 1000. While selling, He sells only 900 grams when he takes the money for 1 kg. Now, according to the problem, he sells at a 8% profit (20% markup, 10% discount). Hence, his selling price is Rs. 1080 for 900 grams. Now, 1100 grams for Rs. 1000 Hence, 1188 grams for Rs. 1080 Selling: 900 grams for Rs. 1080 Hence, % profit = $$\frac{{288}}{{900}}$$ × 100 = 32% (using goods left by goods sold formula).