Q1. Find the gain or loss % when:

C.P. = Rs. 750, S.P.  =  Rs.875

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

C.P. = Rs. 126, S.P.  =  Rs. 94.50

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

C.P. = Rs. 80.40, S.P. =  Rs. 68.34

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

C.P. = Rs. 58.75, S.P. = Rs. 51.70

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

Q2. 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. $= 6020 Rs.$

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

Q3. 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. $= 16422 Rs.$

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

Q4. 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 $= 1360 Rs.$

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

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

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

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

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

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

Q5.  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?

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

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

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

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

Q6 John brought 25kg of rice at Rs. 48/kg and 35kg of rice at Rs. 60/kg. He sold the mixture at Rs. 66/kg. Find his gain or loss %

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

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

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

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

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

Q7 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. $= \frac{4}{5}\textit{x}$

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

Q8. If the selling price of an article is  of its cost price find the gain %.

Let the C.P. be $x$

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

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

Q9 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  $x+\frac{1}{9}x=2250$

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

$x\ =\ 2025\ Rs.$

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

Q10. 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 $x-\frac{1}{16}x\ =\ 195$

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

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

Q11. 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 $\frac{1.1x+99-x}{x}\ =\ \frac{12}{100}$

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

$10x+9900\ =\ 12x$

$x\ =\ 4950\ Rs.$

Q12. 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 $gain\ loss\ \%\ =\ \frac{8}{100}\ =\ \frac{0.92x+56-x}{x}$

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

${16x = 5600}$

${x = 350Rs.}$

Q13. 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 $\ =\ \frac{21}{18}x\ =\ \frac{7}{6}x$

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

Q14. 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   $loss\ \%\ =\ \left(\frac{x-\frac{3}{4}x}{x}\right)\times{}100\ =\ 25\%$

Q15. 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   $\ \ \frac{y}{x}\ =\ \frac{250}{225}$

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

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

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

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

Q16. 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:    $36x-36y = 4y \hspace{5pt} Or$

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

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

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

Q17. 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 =   $\frac{3}{5}Rs.$

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

Q18. 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 %.

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