Question 1: Find the gain or loss % when:

i) C.P. = Rs. $750$, S.P. = Rs. $875$ ii) C.P. = Rs. $126$, S.P. = Rs. $94.50$

iii) C.P. = Rs. $80.40$, S.P. = Rs. $68.34$ iv) C.P. = Rs. $58.75$, S.P. = Rs. $51.70$

i)  P. = Rs. $750$, S.P. = Rs. $875$

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

ii)  P. = Rs. $126$, S.P. = Rs. $94.50$

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

iii)  C.P. = Rs. $80.40$, S.P. = Rs. $68.34$

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

iv)  P. = Rs. $58.75$, S.P. = Rs. $51.70$

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

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

Total C.P. $= 5248+127 = 5375 Rs.$

S.P. $= 6020 Rs.$

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

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

C.P. $= 14625 + 3225 = 17850 Rs.$

S.P. $= 16422 Rs.$

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

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

C.P. of first bat $= 1360 Rs.$

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

C.P. of 2nd bat $= 1040 Rs.$

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

Total C.P. $= 1360 + 1040 = 2400 Rs.$

Total S.P. $= 1564 + 884 = 2448 Rs.$

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

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

$Total\ C.P. = 20 \times 156 = 3120\ Rs.$

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

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

$Total\ S.P. = 1372.8+2246.4 = 3619.2\ Rs.$

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

$\ C.P.1=\ 25 \times 45 = 1200\ Rs.$

$\ C.P.2=\ 35 \times 60 = 2100Rs.$

$\ Total\ C.P. = 1200+2100 = 3300\ Rs.$

$\ Total\ S.P. = 60 \times 66 = 3960\ Rs.$

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

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

Let the C.P. be $x$

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

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

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Question 8: If the selling price of an article is of its cost price find the gain $\%$.

Let the C.P. be $x$

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

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

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

i) The cost of the table          ii) The gain $\%$ earned by the man

S.P. of table = 2250 Rs.

Let the C.P. be $x Rs.$

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

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

$x = 2025\ Rs.$

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

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

Let. the C.P. be $x Rs.$

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

$x = 208\ Rs. = C.P.\ of\ pen$

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

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

Let the C.P. of cycle $x Rs.$

S.P. if sold for 10% gain $1.1 x Rs.$

For 12% gain S.P. $= 1.1x+99$

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

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

$10x+9900 = 12x$

$x = 4950\ Rs.$

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

Let C.P. of the bucket $x Rs.$

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

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

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

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

${16x = 5600}$

${x = 350Rs.}$

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

Let the C.P. of 1 book $= x\ Rs.$

C.P. of 21 books $= 21x\ Rs.$

S.P. of 18 books $= 21x$

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

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

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Question 14: The cost price of $12$ fans is equal to the selling price of $16$ fans. Find the loss or gain $\%$.

Let the C.P. of one Fan $= x\ Rs.$

Therefore S.P. of 16 fans $= 12x\ Rs.$

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

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

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

Let C.P. $= {x}$

Let S.P. $= {y}$

Total C.P. $= 250{x}$

Total S.P. $= 250{y}$

Gain $= 25{y}$

Therefore ${250y-250x = 25y}$

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

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

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

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

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

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

Let C.P. $= x$

Let S.P. $= y$

Total C.P. $= 36x$

Total S.P. $= 36y$

Loss: $36x-36y = 4y \hspace{5pt} Or$

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

$loss\ \% =\Big($ $\frac{x-y}{x}$ $\Big) \times 100$

$=\Big( 1-$ $\frac{9}{10}$ $\Big) \times 100 = 10\%$

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

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

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

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

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

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