\displaystyle \textbf{Question 1: }\text{Find the selling price in each of the following:}
\displaystyle \text{(i) C.P. = Rs. }7640,\quad \text{Gain}=15\%
\displaystyle \text{(ii) C.P. = Rs. }4850,\quad \text{Loss}=12\%
\displaystyle \text{(iii) C.P. = Rs. }720,\quad \text{Loss}=8\frac{3}{4}\%
\displaystyle \text{(iv) C.P. = Rs. }2652,\quad \text{Gain}=16\frac{2}{3}\%
\displaystyle \text{Answer:}

\displaystyle \text{(i) C.P. = Rs. }7640,\quad \text{Gain}=15\%.
\displaystyle \text{S.P.} =\left(1+\frac{15}{100}\right)\times7640.
\displaystyle =\frac{115}{100}\times7640=\text{Rs. }8786.

\displaystyle \text{(ii) C.P. = Rs. }4850,\quad \text{Loss}=12\%.
\displaystyle \text{S.P.} =\left(1-\frac{12}{100}\right)\times4850.
\displaystyle =\frac{88}{100}\times4850=\text{Rs. }4268.

\displaystyle \text{(iii) C.P. = Rs. }720,\quad \text{Loss}=8\frac{3}{4}\%.
\displaystyle 8\frac{3}{4}\%=\frac{35}{4}\%.
\displaystyle \text{S.P.} =\left(1-\frac{\frac{35}{4}}{100}\right)\times720.
\displaystyle =\frac{365}{400}\times720=\text{Rs. }657.

\displaystyle \text{(iv) C.P. = Rs. }2652,\quad \text{Gain}=16\frac{2}{3}\%.
\displaystyle 16\frac{2}{3}\%=\frac{50}{3}\%=\frac{1}{6}.
\displaystyle \text{S.P.} =\left(1+\frac{1}{6}\right)\times2652.
\displaystyle =\frac{7}{6}\times2652=\text{Rs. }3094.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Find the cost price in each of the following:}
\displaystyle \text{(i) S.P. = Rs. }207,\quad \text{Gain}=15\%
\displaystyle \text{(ii) S.P. = Rs. }448.20,\quad \text{Loss}=17\%
\displaystyle \text{(iii) S.P. = Rs. }1479,\quad \text{Gain}=6\%
\displaystyle \text{(iv) S.P. = Rs. }611.80,\quad \text{Loss}=8\%
\displaystyle \text{Answer:}

\displaystyle \text{(i) S.P. = Rs. }207,\quad \text{Gain}=15\%.
\displaystyle \text{C.P.} =\frac{100}{100+15}\times207.
\displaystyle =\frac{100}{115}\times207=\text{Rs. }180.

\displaystyle \text{(ii) S.P. = Rs. }448.20,\quad \text{Loss}=17\%.
\displaystyle \text{C.P.} =\frac{100}{100-17}\times448.20.
\displaystyle =\frac{100}{83}\times448.20=\text{Rs. }540.

\displaystyle \text{(iii) S.P. = Rs. }1479,\quad \text{Gain}=6\%.
\displaystyle \text{C.P.} =\frac{100}{100+6}\times1479.
\displaystyle =\frac{100}{106}\times1479=\text{Rs. }1395.28\text{ (approx.)}.

\displaystyle \text{(iv) S.P. = Rs. }611.80,\quad \text{Loss}=8\%.
\displaystyle \text{C.P.} =\frac{100}{100-8}\times611.80.
\displaystyle =\frac{100}{92}\times611.80=\text{Rs. }665.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{A sells a cycle to B at a profit of }20\%\text{ and B sells}
\displaystyle \text{it to C at a profit of }5\%.\text{ If C pays Rs. }3780,\text{ what did A pay}
\displaystyle \text{for the cycle?}
\displaystyle \text{Answer:}
\displaystyle \text{Let A's cost price be Rs. }x.
\displaystyle \text{A's S.P.}=\text{B's C.P.} =x\left(1+\frac{20}{100}\right)=1.20x.
\displaystyle \text{B's S.P.} =1.20x\left(1+\frac{5}{100}\right).
\displaystyle =1.20x\times1.05=1.26x.
\displaystyle \text{Since C pays Rs. }3780,\quad 1.26x=3780.
\displaystyle x=\frac{3780}{1.26}=3000.
\displaystyle \therefore \text{A paid Rs. }3000\text{ for the cycle}.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{A sold a watch to B at a gain of }12\%\text{ and B sold it}
\displaystyle \text{to C at a loss of }5\%.\text{ If C paid Rs. }5320,\text{ how much did A pay}
\displaystyle \text{for the watch?}
\displaystyle \text{Answer:}
\displaystyle \text{Let A's cost price be Rs. }x.
\displaystyle \text{A's S.P.}=\text{B's C.P.} =x\left(1+\frac{12}{100}\right)=1.12x.
\displaystyle \text{B's S.P.} =1.12x\left(1-\frac{5}{100}\right).
\displaystyle =1.12x\times0.95=1.064x.
\displaystyle \text{Since C pays Rs. }5320,\quad 1.064x=5320.
\displaystyle x=\frac{5320}{1.064}=5000.
\displaystyle \therefore \text{A paid Rs. }5000\text{ for the watch}.
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{A grocer purchased }80\text{ kg of rice at Rs. }27\text{ per kg}
\displaystyle \text{and mixed it with }120\text{ kg of rice purchased at Rs. }32\text{ per kg.}
\displaystyle \text{At what rate per kg should he sell the mixture to gain }16\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of }80\text{ kg of rice}=80\times27=\text{Rs. }2160.
\displaystyle \text{C.P. of }120\text{ kg of rice}=120\times32=\text{Rs. }3840.
\displaystyle \text{Total C.P.}=2160+3840=\text{Rs. }6000.
\displaystyle \text{Total quantity of rice}=80+120=200\text{ kg}.
\displaystyle \text{For a gain of }16\%,\text{ total S.P.} =\frac{116}{100}\times6000.
\displaystyle =\text{Rs. }6960.
\displaystyle \text{S.P. per kg}=\frac{6960}{200}=\text{Rs. }34.80.
\displaystyle \therefore \text{he should sell the mixture at Rs. }34.80\text{ per kg}.
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{A bought two bags for Rs. }1150\text{ each. He sold one}
\displaystyle \text{of them at a gain of }6\%\text{ and the other at a loss of }2\%.\text{ How much}
\displaystyle \text{did he gain on the entire transaction?}
\displaystyle \text{Answer:}
\displaystyle \text{Total C.P.}=1150\times2=\text{Rs. }2300.
\displaystyle \text{S.P. of the first bag} =\frac{106}{100}\times1150=\text{Rs. }1219.
\displaystyle \text{S.P. of the second bag} =\frac{98}{100}\times1150=\text{Rs. }1127.
\displaystyle \text{Total S.P.}=1219+1127=\text{Rs. }2346.
\displaystyle \text{Gain}=2346-2300=\text{Rs. }46.
\displaystyle \therefore \text{he gained Rs. }46\text{ on the entire transaction}.
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{A trader purchased a wall clock and a watch for a total}
\displaystyle \text{of Rs. }5070.\text{ He sold them at a profit of }10\%\text{ on the wall clock}
\displaystyle \text{and }15\%\text{ on the watch. If his total profit was Rs. }699.50,\text{ find}
\displaystyle \text{the cost price of the wall clock and the watch.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the wall clock be Rs. }x.
\displaystyle \text{Let the C.P. of the watch be Rs. }y.
\displaystyle x+y=5070.
\displaystyle \text{Profit on the wall clock}=\frac{10}{100}x=0.10x.
\displaystyle \text{Profit on the watch}=\frac{15}{100}y=0.15y.
\displaystyle \text{Since the total profit is Rs. }699.50,
\displaystyle 0.10x+0.15y=699.50.
\displaystyle \text{Multiplying by }100,\qquad 10x+15y=69950.
\displaystyle \text{Also, multiplying }x+y=5070\text{ by }10,\text{ we get}
\displaystyle 10x+10y=50700.
\displaystyle \text{Subtracting,}\qquad 5y=19250.
\displaystyle y=3850.
\displaystyle x=5070-3850=1220.
\displaystyle \therefore \text{C.P. of the wall clock}=\text{Rs. }1220.
\displaystyle \text{C.P. of the watch}=\text{Rs. }3850.
\displaystyle \\

\displaystyle \textbf{Question 8: }\text{Toffees are bought at }15\text{ for Rs. }20.\text{ How many}
\displaystyle \text{toffees should be sold for Rs. }20\text{ so as to gain }25\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of }15\text{ toffees}=\text{Rs. }20.
\displaystyle \text{C.P. of one toffee}=\frac{20}{15}=\frac{4}{3}\text{ Rs.}
\displaystyle \text{For a gain of }25\%,\text{ S.P. of one toffee}
\displaystyle =\frac{4}{3}\times\frac{125}{100} =\frac{5}{3}\text{ Rs.}
\displaystyle \text{Number of toffees sold for Rs. }20 =20\div\frac{5}{3}.
\displaystyle =20\times\frac{3}{5}=12.
\displaystyle \therefore 12\text{ toffees should be sold for Rs. }20.
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{Two-thirds of a consignment was sold at a profit of }5\%
\displaystyle \text{and the remaining one-third at a loss of }2\%.\text{ If the total profit was}
\displaystyle \text{Rs. }4000,\text{ find the cost price of the entire consignment.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the entire consignment be Rs. }x.
\displaystyle \text{C.P. of the first part}=\frac{2}{3}x.
\displaystyle \text{Profit on the first part} =\frac{5}{100}\times\frac{2}{3}x=\frac{x}{30}.
\displaystyle \text{C.P. of the remaining part}=\frac{1}{3}x.
\displaystyle \text{Loss on the remaining part} =\frac{2}{100}\times\frac{1}{3}x=\frac{x}{150}.
\displaystyle \text{Net profit}=\frac{x}{30}-\frac{x}{150} =\frac{4x}{150}=\frac{2x}{75}.
\displaystyle \frac{2x}{75}=4000.
\displaystyle x=4000\times\frac{75}{2}=150000.
\displaystyle \therefore \text{the cost price of the consignment was Rs. }150000.
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{A grocer bought sugar worth Rs. }4500.\text{ He sold}
\displaystyle \frac{1}{3}\text{ of it at a gain of }10\%.\text{ At what gain percentage should the}
\displaystyle \text{remaining sugar be sold to have a gain of }12\%\text{ on the whole?}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of the sugar}=\text{Rs. }4500.
\displaystyle \text{C.P. of }\frac{1}{3}\text{ of the sugar} =\frac{1}{3}\times4500=\text{Rs. }1500.
\displaystyle \text{C.P. of the remaining sugar} =\frac{2}{3}\times4500=\text{Rs. }3000.
\displaystyle \text{Let the gain on the remaining sugar be }x\%.
\displaystyle \text{S.P. of the first part} =1500\left(1+\frac{10}{100}\right)=\text{Rs. }1650.
\displaystyle \text{For an overall gain of }12\%,\text{ total S.P.}
\displaystyle =4500\left(1+\frac{12}{100}\right)=\text{Rs. }5040.
\displaystyle 1650+3000\left(1+\frac{x}{100}\right)=5040.
\displaystyle 1650+3000+30x=5040.
\displaystyle 30x=390.
\displaystyle x=13.
\displaystyle \therefore \text{the remaining sugar should be sold at a gain of }13\%.
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{A man buys a piece of land for Rs. }38400.\text{ He sells}
\displaystyle \frac{2}{5}\text{ of it at a loss of }6\%.\text{ At what gain percentage should the}
\displaystyle \text{remaining land be sold to have a gain of }10\%\text{ on the whole?}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of the land}=\text{Rs. }38400.
\displaystyle \text{C.P. of }\frac{2}{5}\text{ of the land} =\frac{2}{5}\times38400=\text{Rs. }15360.
\displaystyle \text{C.P. of the remaining }\frac{3}{5}\text{ of the land} =\text{Rs. }23040.
\displaystyle \text{Let the gain on the remaining land be }x\%.
\displaystyle \text{S.P. of the first part} =15360\left(1-\frac{6}{100}\right)=\text{Rs. }14438.40.
\displaystyle \text{For an overall gain of }10\%,\text{ total S.P.}
\displaystyle =38400\left(1+\frac{10}{100}\right)=\text{Rs. }42240.
\displaystyle 14438.40+23040\left(1+\frac{x}{100}\right)=42240.
\displaystyle 14438.40+23040+230.40x=42240.
\displaystyle 230.40x=4761.60.
\displaystyle x=20\frac{2}{3}.
\displaystyle \therefore \text{the remaining land should be sold at a gain of }20\frac{2}{3}\%.
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{By selling a car for Rs. }10416,\text{ a man gains }12\%.
\displaystyle \text{What will be his gain or loss percentage if it is sold for Rs. }9114\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the car be Rs. }x.
\displaystyle x\left(1+\frac{12}{100}\right)=10416.
\displaystyle \frac{112}{100}x=10416.
\displaystyle x=10416\times\frac{100}{112}=\text{Rs. }9300.
\displaystyle \text{If the car is sold for Rs. }9114,\text{ there is a loss}.
\displaystyle \text{Loss}=9300-9114=\text{Rs. }186.
\displaystyle \text{Loss }\%=\frac{186}{9300}\times100=2\%.
\displaystyle \therefore \text{the man incurs a loss of }2\%.
\displaystyle \\

\displaystyle \textbf{Question 13: }\text{A chair is sold for Rs. }2142\text{ at a gain of }5\%.
\displaystyle \text{At what price should it be sold to gain }10\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the chair be Rs. }x.
\displaystyle x\left(1+\frac{5}{100}\right)=2142.
\displaystyle \frac{105}{100}x=2142.
\displaystyle x=2142\times\frac{100}{105}=\text{Rs. }2040.
\displaystyle \text{For a gain of }10\%,\text{ S.P.}
\displaystyle =2040\left(1+\frac{10}{100}\right).
\displaystyle =2040\times1.10=\text{Rs. }2244.
\displaystyle \therefore \text{the chair should be sold for Rs. }2244.
\displaystyle \\

\displaystyle \textbf{Question 14: }\text{A television is sold for Rs. }9360\text{ at a loss of }4\%.
\displaystyle \text{For how much should it be sold to gain }4\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the television be Rs. }x.
\displaystyle x\left(1-\frac{4}{100}\right)=9360.
\displaystyle \frac{96}{100}x=9360.
\displaystyle x=9360\times\frac{100}{96}=\text{Rs. }9750.
\displaystyle \text{For a gain of }4\%,\text{ S.P.}
\displaystyle =9750\left(1+\frac{4}{100}\right).
\displaystyle =9750\times1.04=\text{Rs. }10140.
\displaystyle \therefore \text{the television should be sold for Rs. }10140.
\displaystyle \\

\displaystyle \textbf{Question 15: }\text{A shopkeeper sold two fans for Rs. }1980\text{ each. On one}
\displaystyle \text{he gained }10\%,\text{ while on the other he lost }10\%.\text{ Calculate the gain}
\displaystyle \text{or loss percentage on the whole transaction.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the first fan be Rs. }x.
\displaystyle x\left(1+\frac{10}{100}\right)=1980.
\displaystyle 1.10x=1980.
\displaystyle x=\text{Rs. }1800.

\displaystyle \text{Let the C.P. of the second fan be Rs. }y.
\displaystyle y\left(1-\frac{10}{100}\right)=1980.
\displaystyle 0.90y=1980.
\displaystyle y=\text{Rs. }2200.

\displaystyle \text{Total C.P.}=1800+2200=\text{Rs. }4000.
\displaystyle \text{Total S.P.}=1980+1980=\text{Rs. }3960.
\displaystyle \text{Loss}=4000-3960=\text{Rs. }40.
\displaystyle \text{Loss }\%=\frac{40}{4000}\times100=1\%.
\displaystyle \therefore \text{there is a loss of }1\%\text{ on the whole transaction}.
\displaystyle \\

\displaystyle \textbf{Question 16: }\text{Shanti sold two cameras for Rs. }6555\text{ each. On one}
\displaystyle \text{she lost }5\%,\text{ while on the other she gained }15\%.\text{ Find the gain}
\displaystyle \text{or loss percentage on the whole transaction.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the first camera be Rs. }x.
\displaystyle x\left(1-\frac{5}{100}\right)=6555.
\displaystyle 0.95x=6555.
\displaystyle x=\text{Rs. }6900.

\displaystyle \text{Let the C.P. of the second camera be Rs. }y.
\displaystyle y\left(1+\frac{15}{100}\right)=6555.
\displaystyle 1.15y=6555.
\displaystyle y=\text{Rs. }5700.

\displaystyle \text{Total C.P.}=6900+5700=\text{Rs. }12600.
\displaystyle \text{Total S.P.}=6555+6555=\text{Rs. }13110.
\displaystyle \text{Gain}=13110-12600=\text{Rs. }510.
\displaystyle \text{Gain }\%=\frac{510}{12600}\times100.
\displaystyle =\frac{85}{21}\%=4\frac{1}{21}\%.
\displaystyle \therefore \text{there is a gain of }4\frac{1}{21}\%\text{ on the whole transaction}.
\displaystyle \\

\displaystyle \textbf{Question 17: }\text{By selling }45\text{ lemons for Rs. }40,\text{ a man loses}
\displaystyle 20\%.\text{ How many lemons should he sell for Rs. }24\text{ to gain }20\%\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of one lemon be Rs. }x.
\displaystyle \text{S.P. of one lemon}=\frac{40}{45}=\frac{8}{9}\text{ Rs.}
\displaystyle \text{Since there is a loss of }20\%,
\displaystyle \left(1-\frac{20}{100}\right)x=\frac{8}{9}.
\displaystyle \frac{4}{5}x=\frac{8}{9}.
\displaystyle x=\frac{8}{9}\times\frac{5}{4}=\frac{10}{9}\text{ Rs.}
\displaystyle \text{For a gain of }20\%,\text{ S.P. of one lemon}
\displaystyle =\left(1+\frac{20}{100}\right)\times\frac{10}{9} =\frac{4}{3}\text{ Rs.}
\displaystyle \text{Number of lemons to be sold for Rs. }24 =24\div\frac{4}{3}.
\displaystyle =24\times\frac{3}{4}=18.
\displaystyle \therefore 18\text{ lemons should be sold for Rs. }24.
\displaystyle \\

\displaystyle \textbf{Question 18: }\text{A woman sold a pressure cooker at a loss of }8\%.\text{ Had}
\displaystyle \text{she bought it at }10\%\text{ less and sold it for Rs. }176\text{ more, she would}
\displaystyle \text{have gained }20\%.\text{ Find the original cost price of the pressure cooker.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the original C.P. of the pressure cooker be Rs. }x.
\displaystyle \text{Original S.P.} =x\left(1-\frac{8}{100}\right)=0.92x.
\displaystyle \text{New C.P.} =x\left(1-\frac{10}{100}\right)=0.90x.
\displaystyle \text{New S.P.}=0.92x+176.
\displaystyle \text{With a gain of }20\%,\text{ new S.P.}=1.20\times0.90x=1.08x.
\displaystyle 0.92x+176=1.08x.
\displaystyle 176=0.16x.
\displaystyle x=\frac{176}{0.16}=1100.
\displaystyle \therefore \text{the original cost price of the pressure cooker is Rs. }1100.
\displaystyle \\

\displaystyle \textbf{Question 19: }\text{A man sold a toaster at a profit of }10\%.\text{ Had he}
\displaystyle \text{purchased it for }5\%\text{ less and sold it for Rs. }56\text{ more, he would}
\displaystyle \text{have gained }25\%.\text{ How much did he originally pay for the toaster?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the original C.P. of the toaster be Rs. }x.
\displaystyle \text{Original S.P.} =x\left(1+\frac{10}{100}\right)=1.10x.
\displaystyle \text{New C.P.} =x\left(1-\frac{5}{100}\right)=0.95x.
\displaystyle \text{New S.P.}=1.10x+56.
\displaystyle \text{With a gain of }25\%,\text{ new S.P.}=1.25\times0.95x=1.1875x.
\displaystyle 1.10x+56=1.1875x.
\displaystyle 56=0.0875x.
\displaystyle x=\frac{56}{0.0875}=640.
\displaystyle \therefore \text{the man originally paid Rs. }640\text{ for the toaster}.
\displaystyle \\

\displaystyle \textbf{Question 20: }\text{A shopkeeper sells each of his goods at a gain of }22.5\%.
\displaystyle \text{If, on a particular day, his total sales amounted to Rs. }9408,\text{ find:}
\displaystyle \text{(i) The total cost price of all the goods sold on that day.}
\displaystyle \text{(ii) His total profit for that day.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the total C.P. of the goods sold be Rs. }x.
\displaystyle \text{Since the gain is }22.5\%,
\displaystyle x\left(1+\frac{22.5}{100}\right)=9408.
\displaystyle 1.225x=9408.
\displaystyle x=\frac{9408}{1.225}=\text{Rs. }7680.

\displaystyle \text{(i) }\therefore \text{the total cost price of the goods is Rs. }7680.

\displaystyle \text{(ii) Profit}=9408-7680=\text{Rs. }1728.
\displaystyle \therefore \text{the total profit for the day is Rs. }1728.
\displaystyle \\

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