\displaystyle \textbf{Question 1: }\text{Find the gain or loss percentage in each of the following:}
\displaystyle \text{(i) C.P. = Rs. }750,\quad \text{S.P. = Rs. }875
\displaystyle \text{(ii) C.P. = Rs. }126,\quad \text{S.P. = Rs. }94.50
\displaystyle \text{(iii) C.P. = Rs. }80.40,\quad \text{S.P. = Rs. }68.34
\displaystyle \text{(iv) C.P. = Rs. }58.75,\quad \text{S.P. = Rs. }51.70
\displaystyle \text{Answer:}

\displaystyle \text{(i) C.P. = Rs. }750,\quad \text{S.P. = Rs. }875.
\displaystyle \text{Since S.P.}>\text{C.P., there is a gain}.
\displaystyle \text{Gain}=\text{Rs. }(875-750)=\text{Rs. }125.
\displaystyle \text{Gain }\%=\frac{125}{750}\times100=16\frac{2}{3}\%.

\displaystyle \text{(ii) C.P. = Rs. }126,\quad \text{S.P. = Rs. }94.50.
\displaystyle \text{Since S.P.}<\text{C.P., there is a loss}.
\displaystyle \text{Loss}=\text{Rs. }(126-94.50)=\text{Rs. }31.50.
\displaystyle \text{Loss }\%=\frac{31.50}{126}\times100=25\%.

\displaystyle \text{(iii) C.P. = Rs. }80.40,\quad \text{S.P. = Rs. }68.34.
\displaystyle \text{Since S.P.}<\text{C.P., there is a loss}.
\displaystyle \text{Loss}=\text{Rs. }(80.40-68.34)=\text{Rs. }12.06.
\displaystyle \text{Loss }\%=\frac{12.06}{80.40}\times100=15\%.

\displaystyle \text{(iv) C.P. = Rs. }58.75,\quad \text{S.P. = Rs. }51.70.
\displaystyle \text{Since S.P.}<\text{C.P., there is a loss}.
\displaystyle \text{Loss}=\text{Rs. }(58.75-51.70)=\text{Rs. }7.05.
\displaystyle \text{Loss }\%=\frac{7.05}{58.75}\times100=12\%.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Ranjit purchased a big box for Rs. }5248\text{ and paid}
\displaystyle \text{Rs. }127\text{ for its transportation. He sold it for Rs. }6020.\text{ Find his}
\displaystyle \text{gain percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Purchase price}=\text{Rs. }5248.
\displaystyle \text{Transportation charges}=\text{Rs. }127.
\displaystyle \text{Total C.P.}=5248+127=\text{Rs. }5375.
\displaystyle \text{S.P.}=\text{Rs. }6020.
\displaystyle \text{Gain}=6020-5375=\text{Rs. }645.
\displaystyle \text{Gain }\%=\frac{645}{5375}\times100=12\%.
\displaystyle \therefore \text{Ranjit's gain percentage is }12\%.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Ahmed purchased an old scooter for Rs. }14625\text{ and}
\displaystyle \text{spent Rs. }3225\text{ on its repairs. He then sold it for Rs. }16422.
\displaystyle \text{Find his gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Purchase price}=\text{Rs. }14625.
\displaystyle \text{Repair expenses}=\text{Rs. }3225.
\displaystyle \text{Total C.P.}=14625+3225=\text{Rs. }17850.
\displaystyle \text{S.P.}=\text{Rs. }16422.
\displaystyle \text{Since S.P.}<\text{C.P., Ahmed incurs a loss}.
\displaystyle \text{Loss}=17850-16422=\text{Rs. }1428.
\displaystyle \text{Loss }\%=\frac{1428}{17850}\times100=8\%.
\displaystyle \therefore \text{Ahmed's loss percentage is }8\%.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{A man buys two cricket bats, one for Rs. }1360\text{ and}
\displaystyle \text{the other for Rs. }1040.\text{ He sells the first bat at a gain of }15\%\text{ and}
\displaystyle \text{the second bat at a loss of }15\%.\text{ Find his gain or loss percentage}
\displaystyle \text{on the entire transaction.}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of the first bat}=\text{Rs. }1360.
\displaystyle \text{S.P. of the first bat} =1360\left(1+\frac{15}{100}\right)=\text{Rs. }1564.
\displaystyle \text{C.P. of the second bat}=\text{Rs. }1040.
\displaystyle \text{S.P. of the second bat} =1040\left(1-\frac{15}{100}\right)=\text{Rs. }884.
\displaystyle \text{Total C.P.}=1360+1040=\text{Rs. }2400.
\displaystyle \text{Total S.P.}=1564+884=\text{Rs. }2448.
\displaystyle \text{Gain}=2448-2400=\text{Rs. }48.
\displaystyle \text{Gain }\%=\frac{48}{2400}\times100=2\%.
\displaystyle \therefore \text{there is a gain of }2\%\text{ on the entire transaction}.
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{Mark bought }20\text{ dozen notebooks for Rs. }156\text{ per dozen.}
\displaystyle \text{He sold }8\text{ dozen of them at a gain of }10\%\text{ and the remaining }12
\displaystyle \text{dozen at a gain of }20\%.\text{ Find his gain percentage on the whole transaction.}
\displaystyle \text{Answer:}
\displaystyle \text{Total C.P.}=20\times156=\text{Rs. }3120.
\displaystyle \text{C.P. of }8\text{ dozen}=8\times156=\text{Rs. }1248.
\displaystyle \text{S.P. of }8\text{ dozen} =1248\left(1+\frac{10}{100}\right)=\text{Rs. }1372.80.
\displaystyle \text{C.P. of }12\text{ dozen}=12\times156=\text{Rs. }1872.
\displaystyle \text{S.P. of }12\text{ dozen} =1872\left(1+\frac{20}{100}\right)=\text{Rs. }2246.40.
\displaystyle \text{Total S.P.}=1372.80+2246.40=\text{Rs. }3619.20.
\displaystyle \text{Gain}=3619.20-3120=\text{Rs. }499.20.
\displaystyle \text{Gain }\%=\frac{499.20}{3120}\times100=16\%.
\displaystyle \therefore \text{Mark's gain percentage on the whole transaction is }16\%.
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{John bought }25\text{ kg of rice at Rs. }48\text{ per kg and}
\displaystyle 35\text{ kg of rice at Rs. }60\text{ per kg. He sold the mixture at Rs. }66\text{ per kg.}
\displaystyle \text{Find his gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of }25\text{ kg of rice}=25\times48=\text{Rs. }1200.
\displaystyle \text{C.P. of }35\text{ kg of rice}=35\times60=\text{Rs. }2100.
\displaystyle \text{Total C.P.}=1200+2100=\text{Rs. }3300.
\displaystyle \text{Total quantity of rice}=25+35=60\text{ kg}.
\displaystyle \text{Total S.P.}=60\times66=\text{Rs. }3960.
\displaystyle \text{Gain}=3960-3300=\text{Rs. }660.
\displaystyle \text{Gain }\%=\frac{660}{3300}\times100=20\%.
\displaystyle \therefore \text{John's gain percentage is }20\%.
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{If the selling price of an article is }\frac{4}{5}\text{ of its}
\displaystyle \text{cost price, find the loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the article be Rs. }x.
\displaystyle \text{Then S.P.}=\frac{4}{5}x.
\displaystyle \text{Loss}=x-\frac{4}{5}x=\frac{1}{5}x.
\displaystyle \text{Loss }\% =\frac{\frac{1}{5}x}{x}\times100=20\%.
\displaystyle \therefore \text{the loss percentage is }20\%.
\displaystyle \\

\displaystyle \textbf{Question 8: }\text{If the selling price of an article is }1\frac{1}{3}\text{ times}
\displaystyle \text{its cost price, find the gain percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the article be Rs. }x.
\displaystyle \text{Then S.P.}=1\frac{1}{3}x=\frac{4}{3}x.
\displaystyle \text{Gain}=\frac{4}{3}x-x=\frac{1}{3}x.
\displaystyle \text{Gain }\%=\frac{\frac{1}{3}x}{x}\times100=33\frac{1}{3}\%.
\displaystyle \therefore \text{the gain percentage is }33\frac{1}{3}\%.
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{A man sold a table for Rs. }2250\text{ and gained }\frac{1}{9}
\displaystyle \text{of its cost price. Find:}
\displaystyle \text{(i) The cost price of the table.}
\displaystyle \text{(ii) The gain percentage earned by the man.}
\displaystyle \text{Answer:}
\displaystyle \text{S.P. of the table}=\text{Rs. }2250.
\displaystyle \text{Let the C.P. of the table be Rs. }x.
\displaystyle \text{Gain}=\frac{1}{9}x.
\displaystyle x+\frac{1}{9}x=2250.
\displaystyle \frac{10}{9}x=2250.
\displaystyle x=2250\times\frac{9}{10}=2025.

\displaystyle \text{(i) }\therefore \text{the cost price of the table is Rs. }2025.

\displaystyle \text{(ii) Gain}=2250-2025=\text{Rs. }225.
\displaystyle \text{Gain }\%=\frac{225}{2025}\times100=11\frac{1}{9}\%.
\displaystyle \therefore \text{the gain percentage is }11\frac{1}{9}\%.
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{By selling a pen for Rs. }195,\text{ a man loses }\frac{1}{16}
\displaystyle \text{of its cost price. Find:}
\displaystyle \text{(i) The cost price of the pen.}
\displaystyle \text{(ii) The loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the pen be Rs. }x.
\displaystyle \text{Loss}=\frac{1}{16}x.
\displaystyle x-\frac{1}{16}x=195.
\displaystyle \frac{15}{16}x=195.
\displaystyle x=195\times\frac{16}{15}=208.

\displaystyle \text{(i) }\therefore \text{the cost price of the pen is Rs. }208.

\displaystyle \text{(ii) Loss}=208-195=\text{Rs. }13.
\displaystyle \text{Loss }\%=\frac{13}{208}\times100=6.25\%.
\displaystyle \therefore \text{the loss percentage is }6.25\%.
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{A cycle was sold at a gain of }10\%.\text{ If it had been}
\displaystyle \text{sold for Rs. }99\text{ more, the gain would have been }12\%.\text{ Find the cost}
\displaystyle \text{price of the cycle.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the cycle be Rs. }x.
\displaystyle \text{S.P. at }10\%\text{ gain} =x\left(1+\frac{10}{100}\right)=1.10x.
\displaystyle \text{S.P. at }12\%\text{ gain} =x\left(1+\frac{12}{100}\right)=1.12x.
\displaystyle \text{Difference between the two selling prices}=\text{Rs. }99.
\displaystyle 1.12x-1.10x=99.
\displaystyle 0.02x=99.
\displaystyle x=\frac{99}{0.02}=4950.
\displaystyle \therefore \text{the cost price of the cycle is Rs. }4950.
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{A bucket was sold at a loss of }8\%.\text{ Had it been}
\displaystyle \text{sold for Rs. }56\text{ more, there would have been a gain of }8\%.\text{ What is}
\displaystyle \text{the cost price of the bucket?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of the bucket be Rs. }x.
\displaystyle \text{S.P. at }8\%\text{ loss} =x\left(1-\frac{8}{100}\right)=0.92x.
\displaystyle \text{S.P. at }8\%\text{ gain} =x\left(1+\frac{8}{100}\right)=1.08x.
\displaystyle \text{Difference between the two selling prices}=\text{Rs. }56.
\displaystyle 1.08x-0.92x=56.
\displaystyle 0.16x=56.
\displaystyle x=\frac{56}{0.16}=350.
\displaystyle \therefore \text{the cost price of the bucket is Rs. }350.
\displaystyle \\

\displaystyle \textbf{Question 13: }\text{The selling price of }18\text{ books is equal to the cost}
\displaystyle \text{price of }21\text{ books. Find the gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of one book be Rs. }x.
\displaystyle \text{C.P. of }21\text{ books}=\text{Rs. }21x.
\displaystyle \text{S.P. of }18\text{ books}=\text{Rs. }21x.
\displaystyle \text{S.P. of one book} =\frac{21x}{18}=\frac{7}{6}x.
\displaystyle \text{Since S.P.}>\text{C.P., there is a gain}.
\displaystyle \text{Gain} =\frac{7}{6}x-x=\frac{1}{6}x.
\displaystyle \text{Gain }\% =\frac{\frac{1}{6}x}{x}\times100=16\frac{2}{3}\%.
\displaystyle \therefore \text{the gain percentage is }16\frac{2}{3}\%.
\displaystyle \\

\displaystyle \textbf{Question 14: }\text{The cost price of }12\text{ fans is equal to the selling}
\displaystyle \text{price of }16\text{ fans. Find the gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of one fan be Rs. }x.
\displaystyle \text{C.P. of }12\text{ fans}=\text{Rs. }12x.
\displaystyle \text{S.P. of }16\text{ fans}=\text{Rs. }12x.
\displaystyle \text{S.P. of one fan} =\frac{12x}{16}=\frac{3}{4}x.
\displaystyle \text{Since S.P.}<\text{C.P., there is a loss}.
\displaystyle \text{Loss} =x-\frac{3}{4}x=\frac{1}{4}x.
\displaystyle \text{Loss }\% =\frac{\frac{1}{4}x}{x}\times100=25\%.
\displaystyle \therefore \text{the loss percentage is }25\%.
\displaystyle \\

\displaystyle \textbf{Question 15: }\text{On selling }250\text{ cassettes, a man makes a gain equal}
\displaystyle \text{to the selling price of }25\text{ cassettes. Find the gain percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of one cassette be Rs. }x.
\displaystyle \text{Let the S.P. of one cassette be Rs. }y.
\displaystyle \text{Total C.P. of }250\text{ cassettes}=\text{Rs. }250x.
\displaystyle \text{Total S.P. of }250\text{ cassettes}=\text{Rs. }250y.
\displaystyle \text{Gain}=\text{S.P. of }25\text{ cassettes}=\text{Rs. }25y.
\displaystyle 250y-250x=25y.
\displaystyle 225y=250x.
\displaystyle \frac{y}{x}=\frac{250}{225}=\frac{10}{9}.
\displaystyle \text{Gain }\%=\frac{y-x}{x}\times100.
\displaystyle =\left(\frac{10}{9}-1\right)\times100 =\frac{1}{9}\times100=11\frac{1}{9}\%.
\displaystyle \therefore \text{the gain percentage is }11\frac{1}{9}\%.
\displaystyle \\

\displaystyle \textbf{Question 16: }\text{On selling }36\text{ apples, a vendor loses an amount equal}
\displaystyle \text{to the selling price of }4\text{ apples. Find the loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the C.P. of one apple be Rs. }x.
\displaystyle \text{Let the S.P. of one apple be Rs. }y.
\displaystyle \text{Total C.P. of }36\text{ apples}=\text{Rs. }36x.
\displaystyle \text{Total S.P. of }36\text{ apples}=\text{Rs. }36y.
\displaystyle \text{Loss}=\text{S.P. of }4\text{ apples}=\text{Rs. }4y.
\displaystyle 36x-36y=4y.
\displaystyle 36x=40y.
\displaystyle \frac{y}{x}=\frac{36}{40}=\frac{9}{10}.
\displaystyle \text{Loss }\%=\frac{x-y}{x}\times100.
\displaystyle =\left(1-\frac{9}{10}\right)\times100=10\%.
\displaystyle \therefore \text{the loss percentage is }10\%.
\displaystyle \\

\displaystyle \textbf{Question 17: }\text{Toffees are bought at }2\text{ for a rupee and sold at }5
\displaystyle \text{for Rs. }3.\text{ Find the gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{C.P. of one toffee}=\frac{1}{2}\text{ Rs.}
\displaystyle \text{S.P. of one toffee}=\frac{3}{5}\text{ Rs.}
\displaystyle \text{Since S.P.}>\text{C.P., there is a gain}.
\displaystyle \text{Gain} =\frac{3}{5}-\frac{1}{2}=\frac{1}{10}\text{ Rs.}
\displaystyle \text{Gain }\% =\frac{\frac{1}{10}}{\frac{1}{2}}\times100=20\%.
\displaystyle \therefore \text{the gain percentage is }20\%.
\displaystyle \\

\displaystyle \textbf{Question 18: }\text{Coffee costing Rs. }450\text{ per kg is mixed with chicory}
\displaystyle \text{costing Rs. }225\text{ per kg in the ratio }5:2.\text{ If the mixture is sold}
\displaystyle \text{at Rs. }405\text{ per kg, find the gain or loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Consider }5\text{ kg of coffee and }2\text{ kg of chicory}.
\displaystyle \text{C.P. of }5\text{ kg of coffee}=5\times450=\text{Rs. }2250.
\displaystyle \text{C.P. of }2\text{ kg of chicory}=2\times225=\text{Rs. }450.
\displaystyle \text{C.P. of }7\text{ kg of mixture}=2250+450=\text{Rs. }2700.
\displaystyle \text{C.P. of }1\text{ kg of mixture} =\frac{2700}{7}\text{ Rs.}
\displaystyle \text{S.P. of }1\text{ kg of mixture}=\text{Rs. }405.
\displaystyle \text{Gain} =405-\frac{2700}{7}=\frac{135}{7}\text{ Rs.}
\displaystyle \text{Gain }\% =\frac{\frac{135}{7}}{\frac{2700}{7}}\times100=5\%.
\displaystyle \therefore \text{the gain percentage is }5\%.
\displaystyle \\

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