Practice MCQ Questions and Answer on Profit and Loss

Solution: Advertised price of the item = N ∴ Commission on advertised price of the article = $$\frac{{N \times 23}}{{100}}$$ Price after commission = $$N - \frac{{23N}}{{100}} = \frac{{77N}}{{100}}$$ $$\eqalign{ & \therefore {\text{CP}}\,{\text{of}}\,{\text{the}}\,{\text{item}} \cr & \frac{{\frac{{77N}}{{100}} \times 100}}{{100 + 10}} \cr & = \frac{{77N}}{{110}} \cr & = \frac{{7N}}{{10}} \cr & {\text{Profit}} = \frac{{77N}}{{110}} - \frac{{7N}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{7N}}{{110}} \cr & \Rightarrow 56 = \frac{{7N}}{{110}} \cr & \therefore N = \frac{{56 \times 100}}{7} = 800 \cr} $$

Solution: Let the C.P. of each article be Rs. 100 Then, Cost Price of 16 articles = Rs. (100 × 16) = Rs. 1600 Selling Price of 15 articles $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {1600 \times \frac{{135}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. 2160}}{\text{}} \cr & {\text{S}}{\text{.P}}{\text{. of each article}} \cr & {\text{ = Rs}}{\text{.}}\frac{{2160}}{{15}} \cr & = {\text{Rs}}{\text{. 144}}{\text{}} \cr} $$ If S.P. is Rs. 96, marked price = Rs. 100 If S.P. is Rs. 144, marked price $$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{96}} \times 144} \right) \cr & = {\text{Rs}}{\text{. 150}}{\text{}} \cr} $$ ∴ Marked price = 50% above C.P.

Solution: Selling price of 800 g goods with 20% profit $$ = \frac{{1000\left( {100 + 20} \right)}}{{100}} = {\text{Rs}}{\text{. }}1200$$ Cost price of 800 g goods = Rs. 800 Gain = Selling price - Cost price = 1200 - 800 = 400 $$\eqalign{ & {\text{Gain }}\% = \frac{{400}}{{800}} \times 100\% \cr & = \left( {0.5 \times 100} \right)\% \cr & = 50\% \cr} $$ ∴ His real gain percentage is 50%

Solution: Let the CP1 of Article= 100x Initial SP1 = 100x - 10% of 100x = 100x - 10x = 90x If He sold the Article 10% profit Now SP2 = 100x + 10% of 100x = 100x + 10x =110x According to question SP2 - SP1 = 10 ⇒ 110x - 90x = 10 ⇒ 20x = 10 ⇒ x = $$\frac{1}{2}$$ Initial Cost of Article = 100 × $$\frac{1}{2}$$ = Rs. 50

Solution: $$\eqalign{ & {\text{Let error}} = x{\text{ gms}}{\text{.}} \cr & {\text{Then,}} \cr & = \frac{x}{{1000 - x}} \times 100 = 25 \cr & \Leftrightarrow \frac{{100x}}{{1000 - x}} = 25 \cr & \Leftrightarrow 100x = 25000 - 25x \cr & \Leftrightarrow 125x = 25000 \cr & \Leftrightarrow x = 200 \cr & \therefore {\text{Weight used}} \cr & = (1000 - 200){\text{gms}} \cr & = {\text{800 gms}}. \cr} $$

Solution: Let the original price of salt per kg. is Rs. x So, purchaser can buy $$\frac{{100}}{x}$$ kg. Now, reduction price is 20% Salt per kg. $$ = x \times \frac{{80}}{{100}} = {\text{Rs}}{\text{.}}\,\frac{{4x}}{5}$$ Now purchaser can buy $$\eqalign{ & \frac{{100}}{{\frac{{4x}}{5}}} = \frac{{125}}{x}\,{\text{kg}} \cr & \therefore \frac{{125}}{x} - \frac{{100}}{x} = 4\,{\text{kg}} \cr & \Rightarrow \frac{{25}}{x} = 4 \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,6.25 \cr} $$ Hence the reduced price of salt per kg. $$\eqalign{ & = {\text{Rs}}{\text{.}}\,6.25 \times \frac{{80}}{{100}} \cr & = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$ Alternate: $$\eqalign{ & {\text{Trick}} = \frac{a}{x} \times \frac{{{\text{reduction}}}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{4} \times \frac{{20}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5/{\text{kg.}} \cr} $$

Solution: According to the question, $$\eqalign{ & \frac{{{\text{CP}}}}{{{\text{SP}}}} = \left. {\frac{{20}}{{21}}} \right) + 1 = {\text{Profit}} \cr & {\text{Profit }}\% = \frac{1}{{20}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$

Solution: $$\eqalign{ & {\text{Total Selling Price}} \cr & = {\text{Rs}}{\text{.}}\left( {2 \times 99} \right) \cr & = {\text{Rs}}.198 \cr & {\text{C}}{\text{.P}}{\text{. of first article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}90 \cr & {\text{C}}{\text{.P}}{\text{. of second article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{90}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}110 \cr & {\text{Total C}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left( {90 + 110} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr & \therefore {\text{Loss}} = {\text{Rs}}.\left( {200 - 198} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}2 \cr} $$

Solution:   James   :   Vaibhav Last year →   4 : 5 Let last years total loss ⇒ 90 Last years loss of James $$ = 90 \times \frac{4}{9} = 40$$ Last years loss of Vaibhav $$ = 90 \times \frac{5}{9} = 50$$ James →   Last year   :   Present year   3 : 5 3 ratio → 40 5 ratio → $$\frac{{200}}{3}$$ Vaibhav →   Last year   :   Present year   2 : 3 2 ratio → 50 1 ratio → 25 3 ratio → 75   James   :   Vaibhav Present year →   $$\frac{{200}}{3}$$ : 75   8 : 9 17 ratio → 357000 1 ratio → 21000 8 ratio → 168000

Solution: 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