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

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

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

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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.

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

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

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

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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 $\displaystyle \%$.

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

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

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

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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.

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

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

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

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

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

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

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

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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?

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

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

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

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

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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 $\displaystyle \%$

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

$\displaystyle x = 2025 Rs.$

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

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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 $\displaystyle \%$

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

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

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

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

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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.

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

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

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

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

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

$\displaystyle 10x+9900 = 12x$

$\displaystyle x = 4950 Rs.$

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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?

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

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

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

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

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

$\displaystyle {16x = 5600}$

$\displaystyle {x = 350Rs.}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\displaystyle \text{Gain } = 25{y}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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.

$\displaystyle \text{C.P. of one toffee } = \frac{1}{2} \text{ Rs. }$

$\displaystyle \text{S.P. of one toffee } = \frac{3}{5} \text{ Rs. }$

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

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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 $\displaystyle \%$.

$\displaystyle \text{C.P. of \& kg of mixture } = 450 \times 5+225 \times 2=2700 \text{ Rs. }$
$\displaystyle \text{C.P. of 1 kg of mixture } = \frac{2700}{7} \text{ Rs. }$
$\displaystyle \text{S.P. of 1 kg of mixture } = 405 \frac{Rs}{kg}$
$\displaystyle \text{gain } \% =\Big( \frac{405-\frac{2700}{7}}{2700} \Big) \times 100 = 5\%$