\displaystyle \textbf{Question 1: }\text{The marked price of a refrigerator is Rs. }16450.\text{ The}
\displaystyle \text{shopkeeper offers an off-season discount of }16\%\text{ on it. Find its}
\displaystyle \text{selling price.}
\displaystyle \text{Answer:}
\displaystyle \text{Marked Price}=\text{Rs. }16450.
\displaystyle \text{Discount}=16\%.
\displaystyle \text{Discount amount} =\frac{16}{100}\times16450=\text{Rs. }2632.
\displaystyle \text{Selling Price} =\text{Marked Price}-\text{Discount amount}.
\displaystyle =16450-2632=\text{Rs. }13818.
\displaystyle \therefore \text{the selling price of the refrigerator is Rs. }13818.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{The price of a sweater was reduced by a shopkeeper from}
\displaystyle \text{Rs. }850\text{ to Rs. }731.\text{ Find the rate of discount given by him.}
\displaystyle \text{Answer:}
\displaystyle \text{Marked Price of the sweater}=\text{Rs. }850.
\displaystyle \text{Selling Price}=\text{Rs. }731.
\displaystyle \text{Discount amount} =850-731=\text{Rs. }119.
\displaystyle \text{Discount }\% =\frac{\text{Discount amount}}{\text{Marked Price}}\times100.
\displaystyle =\frac{119}{850}\times100=14\%.
\displaystyle \therefore \text{the rate of discount is }14\%.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Find the rate of discount on a mini toy gun whose selling}
\displaystyle \text{price is Rs. }345\text{ after a discount of Rs. }30\text{ on its marked price.}
\displaystyle \text{Answer:}
\displaystyle \text{Selling Price of the mini toy gun}=\text{Rs. }345.
\displaystyle \text{Discount amount}=\text{Rs. }30.
\displaystyle \text{Marked Price} =\text{Selling Price}+\text{Discount amount}.
\displaystyle =345+30=\text{Rs. }375.
\displaystyle \text{Discount }\% =\frac{\text{Discount amount}}{\text{Marked Price}}\times100.
\displaystyle =\frac{30}{375}\times100=8\%.
\displaystyle \therefore \text{the rate of discount is }8\%.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{After allowing a discount of }15\%,\text{ a baby suit was}
\displaystyle \text{sold for Rs. }1156.\text{ Find its marked price.}
\displaystyle \text{Answer:}
\displaystyle \text{Selling Price of the baby suit}=\text{Rs. }1156.
\displaystyle \text{Discount}=15\%.
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{Discount amount}=\frac{15}{100}x.
\displaystyle \text{Selling Price} =x-\frac{15}{100}x=\frac{85}{100}x.
\displaystyle \frac{85}{100}x=1156.
\displaystyle x=\frac{1156\times100}{85}=1360.
\displaystyle \therefore \text{the marked price of the baby suit is Rs. }1360.
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{A calculator was bought for Rs. }435\text{ after getting a}
\displaystyle \text{discount of }13\%.\text{ Find the marked price of the calculator.}
\displaystyle \text{Answer:}
\displaystyle \text{Selling Price of the calculator}=\text{Rs. }435.
\displaystyle \text{Discount}=13\%\text{ of the Marked Price}.
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{Discount amount}=\frac{13}{100}x.
\displaystyle \text{Selling Price}=\text{Marked Price}-\text{Discount amount}.
\displaystyle 435=x-\frac{13}{100}x.
\displaystyle 435=\frac{87}{100}x.
\displaystyle x=\frac{435\times100}{87}=500.
\displaystyle \therefore \text{the marked price of the calculator is Rs. }500.
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{A dealer marked his goods }35\%\text{ above the cost price}
\displaystyle \text{and allowed a discount of }20\%\text{ on the marked price. Find his gain or}
\displaystyle \text{loss percentage.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the Cost Price be Rs. }x.
\displaystyle \text{Marked Price} =x+\frac{35}{100}x=\frac{135}{100}x.
\displaystyle \text{After a discount of }20\%,\text{ Selling Price}
\displaystyle =\frac{80}{100}\times\frac{135}{100}x=1.08x.
\displaystyle \text{Since S.P.}>\text{C.P., there is a gain}.
\displaystyle \text{Gain}=1.08x-x=0.08x.
\displaystyle \text{Gain }\%=\frac{0.08x}{x}\times100=8\%.
\displaystyle \therefore \text{the dealer makes a gain of }8\%.
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{An article was marked }40\%\text{ above the cost price and}
\displaystyle \text{a discount of }35\%\text{ was given on its marked price. Find the gain or}
\displaystyle \text{loss percentage made by the shopkeeper.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the Cost Price be Rs. }x.
\displaystyle \text{Marked Price} =x+\frac{40}{100}x=\frac{140}{100}x.
\displaystyle \text{After a discount of }35\%,\text{ Selling Price}
\displaystyle =\frac{65}{100}\times\frac{140}{100}x=0.91x.
\displaystyle \text{Since S.P.}<\text{C.P., there is a loss}.
\displaystyle \text{Loss}=x-0.91x=0.09x.
\displaystyle \text{Loss }\%=\frac{0.09x}{x}\times100=9\%.
\displaystyle \therefore \text{the shopkeeper makes a loss of }9\%.
\displaystyle \\

\displaystyle \textbf{Question 8: }\text{A dealer purchased a washing machine for Rs. }7660.
\displaystyle \text{After allowing a discount of }12\%\text{ on its marked price, he gains }10\%.
\displaystyle \text{Find the marked price of the washing machine.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost Price of the washing machine}=\text{Rs. }7660.
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{After a discount of }12\%,\text{ Selling Price}
\displaystyle =x\left(1-\frac{12}{100}\right)=\frac{88}{100}x.
\displaystyle \text{For a gain of }10\%,\text{ Selling Price}
\displaystyle =7660\left(1+\frac{10}{100}\right)=\text{Rs. }8426.
\displaystyle \frac{88}{100}x=8426.
\displaystyle x=\frac{8426\times100}{88}=9575.
\displaystyle \therefore \text{the marked price of the washing machine is Rs. }9575.
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{A shopkeeper bought a sewing machine for Rs. }3750.
\displaystyle \text{After allowing a discount of }10\%\text{ on its marked price, he gains }26\%.
\displaystyle \text{Find the marked price of the sewing machine.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost Price of the sewing machine}=\text{Rs. }3750.
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{After a discount of }10\%,\text{ Selling Price}
\displaystyle =x\left(1-\frac{10}{100}\right)=\frac{90}{100}x.
\displaystyle \text{For a gain of }26\%,\text{ Selling Price}
\displaystyle =3750\left(1+\frac{26}{100}\right).
\displaystyle =3750\times\frac{126}{100}=\text{Rs. }4725.
\displaystyle \frac{90}{100}x=4725.
\displaystyle x=4725\times\frac{100}{90}=5250.
\displaystyle \therefore \text{the marked price of the sewing machine is Rs. }5250.
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{After allowing a discount of }10\%\text{ on the marked price,}
\displaystyle \text{a trader still makes a profit of }17\%.\text{ By what percentage is the marked}
\displaystyle \text{price above the cost price?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{After a discount of }10\%,\text{ Selling Price} =\frac{90}{100}x.
\displaystyle \text{Since the profit is }17\%,\text{ Selling Price} =\frac{117}{100}\times\text{C.P.}
\displaystyle \therefore \text{C.P.} =\frac{100}{117}\times\frac{90}{100}x=\frac{90}{117}x.
\displaystyle \text{Difference between M.P. and C.P.} =x-\frac{90}{117}x.
\displaystyle =\frac{27}{117}x.
\displaystyle \text{Percentage by which M.P. is above C.P.}
\displaystyle =\frac{\frac{27}{117}x}{\frac{90}{117}x}\times100.
\displaystyle =\frac{27}{90}\times100=30\%.
\displaystyle \therefore \text{the marked price is }30\%\text{ above the cost price}.
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{After allowing a discount of }12\%\text{ on the marked price,}
\displaystyle \text{a shopkeeper still gains }21\%.\text{ By what percentage is the marked price}
\displaystyle \text{above the cost price?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the Marked Price be Rs. }x.
\displaystyle \text{After a discount of }12\%,\text{ Selling Price} =\frac{88}{100}x.
\displaystyle \text{Since the gain is }21\%,\text{ Selling Price} =\frac{121}{100}\times\text{C.P.}
\displaystyle \therefore \text{C.P.} =\frac{100}{121}\times\frac{88}{100}x=\frac{88}{121}x.
\displaystyle \text{Difference between M.P. and C.P.} =x-\frac{88}{121}x.
\displaystyle =\frac{33}{121}x.
\displaystyle \text{Percentage by which M.P. is above C.P.}
\displaystyle =\frac{\frac{33}{121}x}{\frac{88}{121}x}\times100.
\displaystyle =\frac{33}{88}\times100=37.5\%.
\displaystyle \therefore \text{the marked price is }37.5\%\text{ above the cost price}.
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{Find a single discount equivalent to two successive}
\displaystyle \text{discounts of }20\%\text{ and }10\%.
\displaystyle \text{Answer:}
\displaystyle \text{Let the Marked Price of the article be Rs. }100.
\displaystyle \text{First discount} =\frac{20}{100}\times100=\text{Rs. }20.
\displaystyle \text{Price after the first discount} =100-20=\text{Rs. }80.
\displaystyle \text{Second discount} =\frac{10}{100}\times80=\text{Rs. }8.
\displaystyle \text{Price after the second discount} =80-8=\text{Rs. }72.
\displaystyle \text{Total discount}=100-72=\text{Rs. }28.
\displaystyle \text{Equivalent single discount} =\frac{28}{100}\times100=28\%.
\displaystyle \therefore \text{the equivalent single discount is }28\%.
\displaystyle \\

\displaystyle \textbf{Question 13: }\text{Find a single discount equivalent to two successive}
\displaystyle \text{discounts of }40\%\text{ and }5\%.
\displaystyle \text{Answer:}
\displaystyle \text{Let the M.P. of the article be Rs. }100.
\displaystyle \text{First discount} =\frac{40}{100}\times100=\text{Rs. }40.
\displaystyle \text{Price after the first discount} =100-40=\text{Rs. }60.
\displaystyle \text{Second discount} =\frac{5}{100}\times60=\text{Rs. }3.
\displaystyle \text{Price after the second discount} =60-3=\text{Rs. }57.
\displaystyle \text{Total discount}=100-57=\text{Rs. }43.
\displaystyle \text{Equivalent single discount} =\frac{43}{100}\times100=43\%.
\displaystyle \therefore \text{the equivalent single discount is }43\%.
\displaystyle \\

\displaystyle \textbf{Question 14: }\text{Find a single discount equivalent to three successive}
\displaystyle \text{discounts of }20\%,\ 5\%\text{ and }1\%.
\displaystyle \text{Answer:}
\displaystyle \text{Let the M.P. of the article be Rs. }100.
\displaystyle \text{First discount} =\frac{20}{100}\times100=\text{Rs. }20.
\displaystyle \text{Price after the first discount} =100-20=\text{Rs. }80.
\displaystyle \text{Second discount} =\frac{5}{100}\times80=\text{Rs. }4.
\displaystyle \text{Price after the second discount} =80-4=\text{Rs. }76.
\displaystyle \text{Third discount} =\frac{1}{100}\times76=\text{Rs. }0.76.
\displaystyle \text{Price after the third discount} =76-0.76=\text{Rs. }75.24.
\displaystyle \text{Total discount} =100-75.24=\text{Rs. }24.76.
\displaystyle \text{Equivalent single discount} =\frac{24.76}{100}\times100=24.76\%.
\displaystyle \therefore \text{the equivalent single discount is }24.76\%.
\displaystyle \\

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