Practice MCQ Questions and Answer on Profit and Loss

Solution: He sold his watch at loss of 5%. If he sells his watch for Rs. 56.25 more, he would gain 10%. It means that 15% = Rs. 56.25. So, 1% = $$\frac{{56.25}}{{15}}$$ 100% = $$\frac{{56.25 \times 100}}{{15}}$$   = Rs. 375 Therefore, the cost price of the watch is Rs. 375

Solution: Let the original price be Rs. 100 Then, Marked price = Rs. 130 Final price = 90% of 90% of Rs. 130 $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{90}}{{100}} \times \frac{{90}}{{100}} \times 130} \right) \cr & = {\text{Rs}}{\text{.105}}{\text{.30}}{\text{}} \cr} $$ ∴ Increase in price = (105.30 - 100)% = 5.3%

Solution: Let cost price of the article is = Rs. 100 Marked price is 10% high of cost price mean = Rs. 110 Discount always given on marked price 10% discount of marked price means $$ = \frac{{10}}{{100}} \times 110 = {\text{ Rs}}{\text{. 11}}$$ ∴ Selling price = Marked price - Discount Selling price = 110 - 11 = Rs. 99 $$\eqalign{ & \therefore {\text{Loss}}\% \cr & = \frac{{{\text{Cost price}} - {\text{Selling price}}}}{{{\text{Cost price}}}} \cr & \Rightarrow {\text{Loss}}\% = \frac{{100 - 99}}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{{100}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr} $$

Solution: Let Cost price = Rs. 100 Then, Selling price = Rs. 120 Let marked price be Rs. x Then, 90% of x = 120 $$\eqalign{ & \Rightarrow x{\text{ = }}\left( {\frac{{120 \times 100}}{{90}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 133\frac{1}{3} \cr & \therefore {\text{Marked price}} \cr & = {\text{33}}\frac{1}{3}\% {\text{ above C}}{\text{P}}{\text{}} \cr} $$

Solution: Let C.P. of clock A be Rs. x and that of clock B be Rs. (650 - x). Then, 120% of x = 75% of (650 - x) $$\eqalign{ & \Rightarrow 650 - x = \frac{{120}}{{75}}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{5}x \cr & \Rightarrow \frac{{13}}{5}x = 650 \cr & \Rightarrow x = \left( {\frac{{650 \times 5}}{{13}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 250 \cr & \therefore {\text{C}}{\text{.P}}{\text{. of A}} = {\text{Rs}}{\text{. }}250 \cr & {\text{C}}{\text{.P}}{\text{. of B}} = {\text{Rs}}{\text{. }}400 \cr} $$

Solution: Let Cost price be Rs. 100 Then, Marked price = Rs. 125 Selling price = 84% of Rs. 125 $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{84}}{{100}} \times 125} \right) \cr & = {\text{Rs}}{\text{.105}}{\text{}} \cr} $$ ∴ Profit % = (105 - 100)% = 5%

Solution: $$\eqalign{ & {\text{C}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {26{\text{ }} \times {\text{ }}20{\text{ }} + {\text{ }}30{\text{ }} \times {\text{ }}36} \right) \cr & = {\text{ }}Rs.{\text{ }}\left( {520{\text{ }} + {\text{ }}1080} \right) \cr & = {\text{ }}Rs.{\text{ }}1600 \cr & {\text{S}}{\text{.P}}{\text{. of 56 kg rice}} \cr & = {\text{ }}Rs.{\text{ }}\left( {56{\text{ }} \times {\text{ }}30} \right) \cr & = {\text{ }}Rs.{\text{ }}1680 \cr & \therefore {\text{Gain}} = \left( {\frac{{80}}{{1600}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$

Solution: 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.

Solution: Total profit = 7.76 In Ist case, (Anand) instead of 1 kg, he gave 950 gm So, profit = 50 gm ⇒ 1000 gm = Rs. 22 1 gm = $$\frac{{22}}{{1000}}$$ 50 gm = $$\frac{{1100}}{{1000}}$$  = 1.1 In Ist case, total profit = 3 + 1.1 = Rs. 4.1 So, left profit = 7.76 - 4.1 = Rs. 3.66 In IInd case, (Sakshi) profit is Rs. 3 as he sold (in Rs. 25) and left Rs. 0.66 is because he sold less of instead of 1000 gm So, Rs. 22 → 1000 gm Rs. 1 → $$\frac{{1000}}{{22}}$$  × 0.66 = 30 gm So he sold 970 gm instead of 1000 gm Answer

Solution: $$\eqalign{ & {\text{S}}{\text{.P}}{\text{. = Rs}}{\text{. }}x \cr & {\text{Profit = 10}}\% \cr & {\text{C}}{\text{.P}}{\text{. = Rs}}{\text{.}}\left( {\frac{{100}}{{110}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{.}}\frac{{10x}}{{11}} \cr & {\text{M}}{\text{.P}}{\text{. = Rs}}{\text{. }}2x, \cr & {\text{Discount = 20}}\% {\text{}} \cr} $$ S.P. at trade fair = 80% of Rs. 2x $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{80}}{{100}} \times 2x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{8x}}{5} \cr & {\text{Profit = Rs}}{\text{.}}\left( {\frac{{8x}}{5} - \frac{{10x}}{{11}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{38x}}{{55}} \cr & \therefore {\text{ Profit }}\% \cr & {\text{ = }}\left( {\frac{{38x}}{{55}} \times \frac{{11}}{{10x}} \times 100} \right)\% \cr & = 76\% \cr} $$