Question 1: Find the gain or loss % when:

i) \displaystyle \text{C.P. = Rs. } 750 , \text{S.P. = Rs. } 875         ii) \displaystyle \text{C.P. = Rs. } 126 , \text{S.P. = Rs. } 94.50

iii) \displaystyle \text{C.P. = Rs. } 80.40 , \text{S.P. = Rs. } 68.34          iv) \displaystyle \text{C.P. = Rs. } 58.75 , \text{S.P. = Rs. } 51.70

Answer:

i) \displaystyle P. = Rs. 750 , \text{S.P. = Rs. } 875

\displaystyle \text{gain } \% = \Big( \frac{875-750}{750} \Big) \times 100 = 16 \frac{2}{3} \%

ii) \displaystyle P. = Rs. 126 , \text{S.P. = Rs. } 94.50

\displaystyle \text{loss } \% = \Big( \frac{126-94.50}{126} \Big) \times 100 = 25\%

iii) \displaystyle \text{C.P. = Rs. } 80.40 , \text{S.P. = Rs. } 68.34

\displaystyle \text{loss } \% = \Big( \frac{80.40-68.34}{80.40} \Big) \times 100 = 15\%

iv) \displaystyle P. = Rs. 58.75 , \text{S.P. = Rs. } 51.70

\displaystyle \text{loss } \% = \Big( \frac{58.75-51.70}{58.75} \Big) \times 100 = 12\%

\displaystyle \\

Question 2: Ranjit purchased a big box for Rs. \displaystyle 5248 and paid Rs. \displaystyle 127 for its transportation. He sold it for Rs. \displaystyle 6020 , Find in gain and loss percentage.

Answer:

\displaystyle \text{Total C.P.  }  = 5248+127 = 5375 \text{ Rs. }

\displaystyle \text{S.P.    } = 6020 \text{ Rs. }

\displaystyle \text{gain } \% =\Big( \frac{6020-5375}{5375} \Big) \times 100 = 12\%

\displaystyle \\

Question 3: Ahmed purchased an old scooter for Rs. \displaystyle 14625 and spent Rs. \displaystyle 3225 on its repair. Then he sold it for Rs. \displaystyle 16422 . find his gain or loss \displaystyle \% .

Answer:

\displaystyle \text{C.P.    } = 14625 + 3225 = 17850 \text{ Rs. }

\displaystyle \text{S.P.    } = 16422 \text{ Rs. }

\displaystyle \text{loss } \% =\Big( \frac{17850-16422}{17850} \Big) \times 100 = 8\%

\displaystyle \\

Question 4: A man buys two cricket bats, one for Rs. \displaystyle 1360 and the other for Rs. \displaystyle 1040 . He sells the first bat at a gain of \displaystyle 15\% and the second bat at a loss of \displaystyle 15\% . Find his gain or loss on entire transaction.

Answer:

\displaystyle \text{C.P. of first bat    } = 1360 \text{ Rs. }

\displaystyle \text{S.P. of first bat } = 1360\Big( 1+ \frac{15}{100} \Big) = 1564 \text{ Rs. }

\displaystyle \text{C.P. of 2nd bat    } = 1040 \text{ Rs. }

\displaystyle S.P. of 2nd bat = 1040\Big( 1- \frac{15}{100} \Big) = 884 \text{ Rs. }

\displaystyle \text{Total C.P.  }  = 1360 + 1040 = 2400 \text{ Rs. }

\displaystyle \text{Total S.P.  }  = 1564 + 884 = 2448 \text{ Rs. }

\displaystyle \text{Hence gain } \% =\Big( \frac{2448-2400}{2400} \Big) \times 100 = 2\%

\displaystyle \\

Question 5: Mark brought \displaystyle 20 dozen note books for Rs. \displaystyle 156 per dozen. He sold \displaystyle 8 dozen of them at \displaystyle 10\% gain and the remaining \displaystyle 12 dozen at \displaystyle 20\% gain. What is his \displaystyle \% in whole transaction?

Answer:

\displaystyle Total C.P. = 20 \times 156 = 3120 \text{ Rs. }

\displaystyle S.P. of 8 dozen = 8 \times 156 \times \Big( 1+ \frac{10}{100} \Big) = 1372.8 \text{ Rs. }

\displaystyle S.P. of 12 dozen = 12 \times 156 \times \Big( 1+ \frac{20}{100} \Big) = 2246.4 \text{ Rs. }

\displaystyle Total S.P. = 1372.8+2246.4 = 3619.2 \text{ Rs. }

\displaystyle \\

Question 6: John brought \displaystyle 25 kg of rice at Rs. \displaystyle 48/kg and \displaystyle 35 kg of rice at Rs. \displaystyle 60/kg . He sold the mixture at Rs. \displaystyle 66/kg . Find his gain or loss \displaystyle \%

Answer:

\displaystyle C.P.1= 25 \times 45 = 1200 \text{ Rs. }

\displaystyle C.P.2= 35 \times 60 = 2100 \text{ Rs. }

\displaystyle Total C.P. = 1200+2100 = 3300 \text{ Rs. }

\displaystyle Total S.P. = 60 \times 66 = 3960 \text{ Rs. }

\displaystyle \text{gain } \% =\Big( \frac{3960-3300}{3300} \Big) \times 100 = 20\%

\displaystyle \\

Question 7: If the selling price of an article is of its cost price, find the loss percent.

Answer:

\displaystyle \text{Let the C.P. be    } x

\displaystyle \text{Then S.P.    } = \frac{4}{5} \textit{x}

\displaystyle \text{loss } \% =\Big( \frac{x-\frac{4}{5}x}{x} \Big) \times 100 = 20\%

\displaystyle \\

Question 8: If the selling price of an article is of its cost price find the \displaystyle \text{Gain }  \% .

Answer:

\displaystyle \text{Let the C.P. be } x

\displaystyle \text{Then S.P.    } = 1 \frac{1}{3} x = \frac{4}{3} x

\displaystyle \text{gain } \% =\Big( \frac{\frac{4}{3}x-x}{x} \Big) \times 100 = 33\frac{1}{3}\%

\displaystyle \\

Question 9: A man sold a table for Rs. \displaystyle 2250 and gained of its cost price. Find

i) The cost of the table       ii) The \displaystyle \text{Gain }  \% earned by the man

Answer:

\displaystyle \text{S.P. of table     = 2250 Rs. }

\displaystyle \text{Let the C.P. be    } x \text{ Rs. }

\displaystyle \text{Therefore }  x+ \frac{1}{9} x=2250

\displaystyle \frac{10}{9} x = 2250

\displaystyle x = 2025 Rs.

\displaystyle \text{gain } \% =\Big( \frac{2250-2025}{2025} \Big) \times 100 =11\frac{1}{9}\%

\displaystyle \\

Question 10: By selling a pen for Rs. \displaystyle 195 , man losses of what it costs him. Find i.) The cost price of the pen ii.) Loss \displaystyle \%

Answer:

\displaystyle \text{Let. the C.P. be    } x \text{ Rs. }

\displaystyle \text{Hence    } x- \frac{1}{16} x = 195

\displaystyle x = 208 Rs. = \text{C.P. of pen}

\displaystyle \text{loss } \% = \Big( \frac{208-195}{208} \Big) \times 100 = 6.25\%

\displaystyle \\

Question 11: A cycle was sold at a gain of \displaystyle 10\% it had been sold for Rs. \displaystyle 99 more; the gain would have been \displaystyle 12\% . Find the cost of the cycle.

Answer:

\displaystyle \text{Let the C.P. of cycle    } x Rs.

\displaystyle \text{S.P. if sold for 10\%    } \text{Gain }  1.1 x Rs.

\displaystyle \text{For 12\% gain S.P.    } = 1.1x+99

\displaystyle \text{Hence    } \frac{1.1x+99-x}{x} = \frac{12}{100} 

\displaystyle 110x+9900-100x = 12x

\displaystyle 10x+9900 = 12x

\displaystyle x = 4950 Rs.

\displaystyle \\

Question 12: A bucket was sold at a loss of \displaystyle 8\% . Had it beer sold for Rs. \displaystyle 56 more, there would have been a gain of \displaystyle 8\% . What is the cost price of the bucket?

Answer:

\displaystyle \text{Let C.P. of the bucket    } x Rs.

\displaystyle S.P.1 = 0.92{x}

\displaystyle S.P.2 = 0.92{x}+56

\displaystyle \text{Hence gain loss} \% = \frac{8}{100} = \frac{0.92x+56-x}{x}

\displaystyle {8x = 92x+5600-100x}

\displaystyle {16x = 5600}

\displaystyle {x = 350Rs.}

\displaystyle \\

Question 13: The selling price of \displaystyle 18 books is equal to the cost price of \displaystyle 21 books. Find the gain or loss \displaystyle \% .

Answer:

\displaystyle \text{Let the C.P. of 1 book    } = x Rs.

\displaystyle \text{C.P. of 21 books    } = 21x Rs.

\displaystyle \text{S.P. of 18 books    } = 21x

\displaystyle \text{Therefore S.P. of 1 book    } = \frac{21}{18} x = \frac{7}{6} x

\displaystyle \text{gain } \% =\Big( \frac{\frac{7}{6}x-x}{x} \Big) \times 100 = 16 \frac{2}{3} \%

\displaystyle \\

Question 14: The cost price of \displaystyle 12 fans is equal to the selling price of \displaystyle 16 fans. Find the loss or \displaystyle \text{Gain }  \% .

Answer:

\displaystyle \text{Let the C.P. of one Fan    } = x \text{ Rs. }

\displaystyle \text{Therefore S.P. of 16 fans    } = 12x \text{ Rs. }

\displaystyle \text{S.P. of 1 fan    } = \frac{12}{16} x = \frac{3}{4} x

\displaystyle \text{Therefore }  \text{loss } \% =\Big( \frac{x-\frac{3}{4}x}{x} \Big) \times 100 = 25\%

\displaystyle \\

Question 15: On selling \displaystyle 250 cassettes, a man had a gain equal to the selling price of \displaystyle 25 cassettes. Find the \displaystyle \text{Gain }  \% .

Answer:

\displaystyle \text{Let C.P.   }  = {x}

\displaystyle \text{Let S.P.   }  = {y}

\displaystyle \text{Total C.P.  }  = 250{x}

\displaystyle \text{Total S.P.  }  = 250{y}

\displaystyle \text{Gain }  = 25{y}

\displaystyle \text{Therefore }  {250y-250x = 25y}

\displaystyle \text{Or   }  \frac{y}{x} = \frac{250}{225} 

\displaystyle \text{gain } \% =\Big( \frac{y-x}{x} \Big) \times 100

\displaystyle =\Big( \frac{250}{225} -1\Big) \times 100

\displaystyle = \frac{25 \times 100}{225} 

\displaystyle = 11 \frac{1}{9} \%

\displaystyle \\

Question 16: On selling \displaystyle 36 apples, a vendor losses the selling price of \displaystyle 4 oranges. Find the loss percent.

Answer:

\displaystyle \text{Let C.P.   }  = x

\displaystyle \text{Let S.P.   }  = y

\displaystyle \text{Total C.P.  }  = 36x

\displaystyle \text{Total S.P.  }  = 36y

\displaystyle \text{Loss:  }  36x-36y = 4y \hspace{5pt}\text{ or }

\displaystyle \frac{y}{x} = \frac{36}{40} = \frac{9}{10} 

\displaystyle \text{loss } \% =\Big( \frac{x-y}{x} \Big) \times 100 \displaystyle =\Big( 1- \frac{9}{10} \Big) \times 100 = 10\%

\displaystyle \\

Question 17: Toffees are brought at \displaystyle 2 for a rupee and sold at \displaystyle 5 for Rs. \displaystyle 3 . Find the gain or loss percent.

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{Gain} \% =\Big( \frac{\frac{3}{5}-\frac{1}{2}}{\frac{1}{2}} \Big) \times 100 = 20 \%

\displaystyle \\

Question 18: Coffee costing Rs. \displaystyle 450/kg was mixed with Chicory costing Rs. \displaystyle 225/kg in the ration of \displaystyle 5:2 for a certain blend. If the mixture was sold at Rs. \displaystyle 405/kg , find the gain or loss \displaystyle \% .

Answer:

\displaystyle \text{C.P. of \& kg of mixture    } = 450 \times 5+225 \times 2=2700 \text{ Rs. }

\displaystyle \text{C.P. of 1 kg of mixture    } = \frac{2700}{7} \text{ Rs. }

\displaystyle \text{S.P. of 1 kg of mixture    } = 405 \frac{Rs}{kg} 

\displaystyle \text{gain } \% =\Big( \frac{405-\frac{2700}{7}}{2700} \Big) \times 100 = 5\%