Question 1: The marked price of a refrigerator is Rs. \displaystyle 16450 . The shopkeeper offers on off-season discount of \displaystyle 16 \% on it. Find its selling price.

Answer:

Marked Price \displaystyle = 16450 \text{ Rs. }

\displaystyle \text{Off season discount    } = 16 \%

\displaystyle \text{Discount    } = \frac{16}{100} \times \text{ Market Price } = \frac{16}{100} \times 16450  = 2632 \text{ Rs. }

\displaystyle \text{Selling Price } = 16450-2632 = 13818 \text{ Rs. }

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Question 2: The price of a sweater was slashed down by a shopkeeper from Rs. \displaystyle 850 to Rs. \displaystyle 731 . Find the rate of discount given by him.

Answer:

\displaystyle \text{Market Price of the sweater    } = 850 \text{ Rs. }

\displaystyle \text{Selling Price    } = 731 \text{ Rs. }

\displaystyle \text{Discount = Marked Price  -  Selling Price } = 850 - 731 = 119 \text{ Rs. }

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Question 3: Find the rate of discount being given on mini toy-gun whose selling price is Rs. \displaystyle 345 after deducting a discount being given on a mini toy-gun whose selling price is Rs. \displaystyle 345 after deducting a discount of Rs. \displaystyle 30 on its marked price.

Answer:

\displaystyle \text{Selling Price of a mini toy gun    } = 345 \text{ Rs. }

\displaystyle \text{Discount    } = 30 \text{ Rs. }

\displaystyle \text{Marked Price  =  Selling Price  + Discount } = 345 + 30 = 375 \text{ Rs. }

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Question 4: After allowing a discount of \displaystyle 15 \% , a baby-suit was sold for Rs. \displaystyle 1156 . Find its marked price.

Answer:

Selling Price of a baby suit \displaystyle = 1156 \text{ Rs. }

Discount \displaystyle = 15 \%

Let Marked Price \displaystyle = Rs. x

\displaystyle \text{Discount    } = \frac{15}{100} \times x

\displaystyle \text{Selling Price    } = x - \frac{15x}{100} = \frac{85}{100} x

Equating the above with actual selling price

\displaystyle \frac{85}{100} x = 1156

\displaystyle x ( \frac{1156 \times 100}{85} ) = 1360

Marked Price of the body Suit \displaystyle = 1360 \text{ Rs. }

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Question 5: A calculator was bought for Rs. \displaystyle 435 after getting a discount of \displaystyle 13 \% . Find the marked price of the calculator.

Answer:

\displaystyle \text{Purchase Price of the calculator  = Selling Price of the calculator = 435}  \text{ Rs. }

Discount \displaystyle = 13 \% on the marked price

Let Marked Price \displaystyle = x \text{ Rs. }

\displaystyle \text{Discount    } = \frac{13}{100} x

M.P. \displaystyle = S.P. \displaystyle + Discount

\displaystyle x = 435+ \frac{13}{100} x

\displaystyle \text{ or }  x - \frac{13}{100} x = 435

\displaystyle \text{ or }  \frac{87}{100} x = 435

\displaystyle \text{ or }  x = \frac{435 \times 100}{87} = 500

\displaystyle \text{Marked price of the calculate    } = 500 \text{ Rs. }

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Question 6: A dealer marked his goods \displaystyle 35 \% above cost price and allowed a discount of \displaystyle 20 \% on the market price. Find his gain or loss per cent.

Answer:

\displaystyle \text{Let Cost Price    } = x \text{ Rs. }

\displaystyle \text{Marked Price    } = x + \frac{35}{100} x = \frac{135}{100} x

\displaystyle \text{Discount    } = 20 \%  \text{ on M.P.} = ( \frac{20}{100} ) \times M.P. = \ ( \frac{20}{100} ) \times ( \frac{135}{100} )x

\displaystyle \text{S.P. = M.P. - Discount} = \frac{135}{100} x- \frac{20}{100} \times \frac{135}{100} x = \frac{80}{100} \times \frac{135}{100} x

\displaystyle \text{Profit    } = \text{S.P. - Cost \ Price }  = \frac{80 \times 135}{100 \times 100} x-x = 1.08x - x = 0.08 x

\displaystyle \% \text{ age profit } = \frac{\text{Profit}}{\text{C.P.}} \times 100 = \frac{0.08x}{x} \times 100 = 8 \%

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Question 7: An article was marked \displaystyle 40 \% above cost price and a discount of \displaystyle 35 \% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.

Answer:

\displaystyle \text{Let Cost Price    } = Rs. x

\displaystyle \text{Marked Price    } = x + \frac{40}{100} x = \frac{140}{100} x

\displaystyle \text{Discount    } = 35 \% \text{ of the M.P. } = \frac{35}{100} \times \frac{140}{100} x

\displaystyle \text{S.P. = M.P. - Discount} = \frac{140x}{100} - \frac{35}{100} \times {} \frac{140}{100} x = \frac{65}{100} \times \frac{140}{100} x

\displaystyle \text{ Gain = Cost - S.P. }= x - \frac{65}{100} \times \frac{140}{100} x = x - 0.91 x = 0.09x

\displaystyle \% \text{Gain } = \frac{0.09x}{x} \times 100 = 9 \%

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Question 8: A dealer purchased a washing machine for Rs. \displaystyle 7660 . after allowing a discount of \displaystyle 12 \% on its marked price, he gains \displaystyle 10 \% . Find the marked price.

Answer:

The cost price \displaystyle = 7660 \text{ Rs. }

Let M.P. \displaystyle = x \text{ Rs. }

\displaystyle \text{Discount  } = \frac{12}{100}

\displaystyle \text{S.P. = M.P. - Discount = Rs. } x - \frac{12}{100} x = Rs. \frac{88}{100} x

\displaystyle \text{Gain is  10 \% of the cost Price = Rs. } \frac{10}{100} \times 7660 = 766 \text{ Rs. }

\displaystyle \text{Gain = S.P. - Cost Price = }  \frac{88}{100} x - 7660

\displaystyle 766 = \frac{88}{100} x-7660

\displaystyle \frac{88}{100} x = 7660+766 = 8426

\displaystyle x = ( \frac{8426 \times 100}{88} ) = 9575 \text{ Rs. }

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Question 9: A shopkeeper bought a sewing machine for Rs. \displaystyle 3750 . after allowing a discount of \displaystyle 10 \% on its marked price, he gains \displaystyle 26 \% . Find the marked price of the sewing machine.

Answer:

\displaystyle \text{Cost of the sewing machine    } = 3750 \text{ Rs. }

\displaystyle \text{Let Mark Price.    } = x \text{ Rs. }

\displaystyle \text{Discount    } = \frac{10}{100} x

\displaystyle \text{Selling Price    } = x - \frac{10}{100} x = \frac{90}{100} x

\displaystyle \text{Gain  = Selling Price - Cost Price } = ( \frac{90}{100} x - 3750) … … … … … i)

\displaystyle \text{Gain is  26 \% of the CP  =} \frac{26}{100} \times 3750 = 975 … … … … … ii)

Equating i) and ii)

\displaystyle \frac{90}{100} x-3750 = 975

\displaystyle \text{ or }  x = (975 +3750) \times \frac{100}{90} = 5250

\displaystyle \text{Marked Price  } = 5250 \text{ Rs. }

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Question 10: After allowing a discount of \displaystyle 10 \% on the marked price, a trader still makes a profit of \displaystyle 17 \% . By what per cent is the marked price above cost price?

Answer:

\displaystyle \text{ Let Marked Price  } = x \text{ Rs. }

\displaystyle \text{S.P. }  = x - \text{Discount of 10 \%  of } x = x- \frac{10}{100} x = \frac{90}{100} x

\displaystyle \text{ \% Gain }= \frac{S.P-C.P}{C.P} \times x

\displaystyle \text{ (\% gain)(C.P.) = S.P. } \times 100 - C.P.\times 100

\displaystyle \text{ (\% gain) (C.P.) +C.P. } \times 100 = S.P.100

\displaystyle \text{C.P.    } = \frac{\text{S.P. } \times 100}{ \text{\% gain }+100} = \frac{x\frac{90}{100} \times 100}{17+100} = \frac{90}{117} x

\displaystyle \text{Difference between M.P. and C.P.    } = x - \frac{90}{117} x = \frac{27}{117} x

\displaystyle \text{ \%  age of difference in marked price over cost price } =\frac{ \frac{27}{117}x}{ \frac{90}{117}x} \times 100 = 30 \%

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Question 11: After allowing a discount of \displaystyle 12 \% on the marked price, a shopkeeper still gains \displaystyle 21 \% . By what per cent is the marked price above cost price?

Answer:

\displaystyle \text{Let marked price in }  x \text{ Rs. }  

\displaystyle \text{S.P. } = x-12 \%  \text{ discount on }  x = x - \frac{12}{100} x = \frac{88}{100} x

\displaystyle \text{C.P. } = \frac{S.P. \times 100}{ \% gain\ +100} = \frac{\frac{88}{100}x \times 100}{21+100} = \frac{88}{121} x

\displaystyle \text{Difference between M.P. and C.P.    } = x - \frac{88}{121} x = \frac{33}{121} x

 \displaystyle \text{\%  of difference in marked price over cost price }  = \frac{\frac{33}{121}x}{\frac{88}{121}x} \times 100 = \frac{300}{8} = 37.5 \%

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Question 12: Find a single discount equivalent to two successive discounts of \displaystyle 20 \% and \displaystyle 10 \%

Answer:

Let the M.P. of the article be \displaystyle 100 \text{ Rs. }  

\displaystyle 1^{st} Discount is \displaystyle 20 \% , Discount \displaystyle = 20 \text{ Rs. }  

Reduced Price after the first discount \displaystyle = Rs. (100-20) = 80 \text{ Rs. }  

\displaystyle 2^{nd} \text{   discount is  10 \% of } 80 = \frac{10}{100} \times 80 = 8 \text{ Rs. }

Price after the second discount \displaystyle = 80 - 8 = 72 \text{ Rs. }

S.P. of the article \displaystyle 72 \text{ Rs. }  

Net discount \displaystyle = 100 - 72 = 28 Rs. 

Thus, net discount on M.P. of Rs. \displaystyle 100 is \displaystyle 28 \text{ Rs. }  

Single discount equivalent to given successive discounts \displaystyle = 28 \%

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Question 13: Find a single discount equivalent to two successive discounts of \displaystyle 40 \% and \displaystyle 5 \% .

Answer:

\displaystyle \text{Let the M.P. of an article is Rs.    } 100

\displaystyle \text{Discount on it is    } = 40 \% \ of \ 100 = 40 \text{ Rs. }

\displaystyle \text{Reduced Price after first discount    } = (100-40) = 60 \text{ Rs. }

\displaystyle \text{Next Discount is    } = 5 \% \ of \ 60

\displaystyle ( \frac{5}{100} \times 60) = 3 \text{ Rs. }  

\displaystyle \text{Price after second Discount    } = 60-3 = 57 \text{ Rs. }

\displaystyle \text{That is S.P.    } = 57 \text{ Rs. }  

\displaystyle \text{Net Discount    } = M.P. -S.P. = 100 -57 = 43 \text{ Rs. }  

Thus, net discount on MP. of \displaystyle 100 \text{ Rs. } is \displaystyle 43. \text{ Rs. }  

Single discount equivalent to given successive discounts = 43 \% $

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Question 14: Find a single discount equivalent to three successive discounts of \displaystyle 20 \% , 5 \% and \displaystyle 1 \%

Answer:

\displaystyle \text{Let the M.P. of an article in Rs.    } 100

\displaystyle \text{It discount on it is    } = 20 \% of \displaystyle 100 = 20 \text{ Rs. }

\displaystyle \text{Reduced price after the its discount  } = 100 - 20 = 80 \text{ Rs. }

\displaystyle \text{Second discount on it    } = 5 \% of \ 80 = \frac{5}{100} \times 80 = 4 \text{ Rs. }

\displaystyle \text{Price after second discount    } = 80-4 = 76 \text{ Rs. }

\displaystyle \text{Third discount on it is 1 \%  of } 76 = \frac{1}{100} \times 76 = 0.76 \text{ Rs. }

\displaystyle \text{Price after Third discount    } = 76-0.76 = 75.24 \text{ Rs. }

\displaystyle \text{ S.P. of the article  } = 75.24 \text{ Rs. }

\displaystyle \text{ Thus, net discount on M.P. of Rs.  } 100 in Rs. \displaystyle 24.76

\displaystyle \text{Single discount equivalent to given successive discounts  } = 24.76 \%