Question 13 Marks
On selling a bat for $Rs. 486$ a man loses $10\%.$ Find the cost price of the bat.
Answer$SP$ of the bat $= Rs. 486$
Loss $= 10\%$
$CP$ of the bat $=\Big\{\frac{100}{(100-\text{Loss%)}}\times\text{SP}\Big\}$
$=\Big\{\frac{100}{(100-10)}\times486\Big\}$
$=\frac{48600}{90}$
$=\text{Rs. }540$
$CP$ of the bat $= Rs. 540$
View full question & answer→Question 23 Marks
Find the $C.P.$ when: $S.P. = Rs. 1755,$ gain $=12\frac{1}{2}\%$
Answer$S.P. = Rs. 1755$
Gain $\%=12\frac{1}{2}\%$
$=\frac{25}{2}\%$
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100+\text{gain%}}$
$=\frac{1755\times100}{100+\frac{25}{2}}$
$=\text{Rs. }\frac{1755\times100}{\frac{200+25}{2}}$
$=\frac{1755\times100\times2}{225}$
$=\text{Rs. }\frac{195\times4\times2}{1}$
$=\text{Rs. }1560$
View full question & answer→Question 33 Marks
Sudhir bought an almirah for $Rs. 13600$ and spent $Rs. 400$ on its transportation. He sold it for $Rs. 16800.$ Find his gain percent.
Answer$C.P.$ of an almirah $= Rs. 13600$
Amount spent on transportation $= Rs. 400$
Total cost price $(CP) = Rs. 13600 + Rs. 400 = Rs. 14000$
$SP = Rs. 16800$
Total gain $= SP - CP$
$= Rs. 16800 - Rs. 14000 = Rs. 2800$
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{2800\times100}{14000}$
$=20\%$
View full question & answer→Question 43 Marks
If the selling price of $10$ pens is equal to the cost price of $14$ pens, find gain percent.
AnswerLet the cost of each pen be $Rs. 1 $
$CP$ of $10$ pens $= Rs. 10 $
$SP$ of $10$ pens $= CP$ of $14$ pens $= Rs. 14$
Gain $= SP - CP = 14 - 10 = Rs. 4$
$\text{Gain}\%=\Big(\frac{\text{Gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{4}{10}\times100\Big)\%$
$=40\%$
View full question & answer→Question 53 Marks
Find the $SP$ when: $C.P. = Rs. 950,$ gain $= 6\%$
Answer$C.P. = Rs. 950$ Gain$\% = 6\%$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{950(100+6)}{100}$
$=\frac{950\times106}{100}$
$=\text{Rs. }1007$
View full question & answer→Question 63 Marks
Find the $C.P.$ when: $SP = Rs. 5600,$ loss $=6\frac{2}{3}\%$
Answer$S.P. = Rs. 5600$
Loss $=6\frac{2}{3}\%$
$=\frac{20}{3}\%$
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100-\text{Loss%}}$
$=\text{Rs. }\frac{5600\times100}{100-\frac{20}{3}}$
$=\text{Rs. }\frac{5600\times100\times3}{280}$
$=\text{Rs. }6000$
View full question & answer→Question 73 Marks
Ravi purchased an old house for $Rs. 765000$ and spent $Rs. 115000$ on its repairs, then, he sold it at a gain of $5\%.$ How much did he get$?$
Answer$CP$ of an old house $= Rs. 765000$
Amount spent on repairs $= Rs. 115000$
Total cost price $(CP) = Rs. 765000 + Rs. 115000 = Rs. 880000$
Gain $= 5\%$
$\therefore\text{SP of the house}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{880000\times(100+5)}{14000}$
$=\text{Rs. }\frac{880000\times105}{100}$
$=\text{Rs. }924000$
View full question & answer→Question 83 Marks
On selling an exhaust fan for $Rs. 7350,$ a man gains $\frac{1}{6}$ of its cost price. Find the cost price of the fan.
Answer$SP$ of an exhaust fan $= Rs. 7350$
Gain $=\frac{1}{6}$ of $CP$
Then gain $=\frac{1}{6}$ of $\text{x}=\text{Rs. }\frac{\text{x}}{6}$
$\therefore\text{SP}=\text{x}+\frac{\text{x}}{6}$
$=\frac{7\text{x}}{6}$
Now $\frac{7\text{x}}{6}=7350$
$\Rightarrow\text{x}=\frac{7350\times6}{7}$
$=\text{Rs. }1050\times6$
$=\text{Rs. }6300$
Cost price of the fan $= Rs. 6300$
View full question & answer→Question 93 Marks
Find the $SP$ when: $C.P. = Rs. 9600,$ gain $=16\frac{2}{3}\%$
Answer$C.P. = Rs. 9600$ Gain$\% =16\frac{2}{3}\%$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100+\text{gain%})}{100}$
$=\frac{950\Big(100+\frac{50}{3}\Big)}{100}$
$=\frac{9600\times350}{100\times3}$
$=\text{Rs. }11200$
View full question & answer→Question 103 Marks
The selling price of $12$ pens is equal to the cost price of $15$ pens. Find the gain percent.
AnswerLet the cost price of the pen be $Rs.1.$
Cost price of $12$ pens $= Rs. 12$
$SP$ of $12$ pens $= CP$ of $15$ pens $= Rs. 15$
Gain $= SP - CP = Rs. (15 - 12) = Rs. 3$
$\therefore\text{Gain}\%=\Big(\frac{\text{Gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{3}{12}\times100\Big)\%$
$=25\%$ Gain$\% = 25\%$
View full question & answer→Question 113 Marks
Find the $C.P.$ when: $S.P. = Rs. 924,$ gain $= 10\%$
Answer$S.P. = Rs. 924$
Gain$\% = 10\%$
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100+\text{gain%}}$
$=\text{Rs. }\frac{924\times100}{100+10}$
$=\text{Rs. }\frac{924\times100}{110}$
$=\text{Rs. }840$
View full question & answer→Question 123 Marks
By selling a chair for $Rs. 1375$ a man gains $10\%$. Find its cost price.
Answer$SP$ of the chair $= Rs. 1375$
Gain$\% = 10$
$CP$ of the chair $=\Big\{\frac{100}{(100+\text{Gsin%})}\times\text{SP}\Big\}$
$=\Big\{\frac{100}{(100+10)}\times1375\Big\}$
$=\frac{137500}{110}$
$\text{Rs. }1250$
View full question & answer→Question 133 Marks
On selling a watch for $Rs. 11400$, a shopkeeper loses $5\%.$ For how much did he purchase it$?$
Answer$SP$ of a watch $= Rs. 11400$
Loss $= 5\%$
$\text{CP of a watch}=\frac{\text{SP}\times100}{100-\text{loss%}}$
$=\frac{11400\times100}{100-5}$
$=\text{Rs. }\frac{11400\times100}{95}$
$=\text{Rs. }12000$
View full question & answer→Question 143 Marks
Find the gain or loss per cent when: $CP = Rs. 1650$ and $SP = Rs. 1452$
Answer$C.P. = Rs. 1650$
$SP = Rs. 1452$
Gain $= CP - SP = Rs. 1650 - Rs. 1452 = Rs. 198$
$\therefore\text{Loss%}=\frac{\text{Total Loss}\times100}{\text{CP}}$
$=\frac{198\times100}{1650}$
$=12\%$
View full question & answer→Question 153 Marks
Mohit sold a watch to Karim at a gain of $10\%$ and Karim sold it to Rahim at a gain of $4\%.$ If Rahim pays $Rs. 14300$ for it, for how much did Mohit purchase it$?$
AnswerLet $CP$ of watch for Mohit $= Rs. 100$
Gain $=10\%$
$SP$ for Mohit $= Rs. 100 + 10 = Rs. 110$
$CP$ for Karim $= Rs. 110$ Gain $= 4\%$
$SP$ for karim, $=\text{Rs. }\frac{110\times(100+4)}{100}$
$=\text{Rs. }\frac{110\times104}{100}$
$=\text{Rs. }\frac{1144}{10}$ Or $CP$ for Rahime is $Rs. \frac{1144}{10},$
the $CP$ For Mohit $= Rs. 100$ And
if $CP$ for Rahim is $Rs. 14300,$
then $CP$ Mohit $= \text{Rs. }\frac{100\times14300\times10}{1144}$
$=\text{Rs. }12500$
View full question & answer→Question 163 Marks
A vendor buys lemons at $Rs. 25$ per dozen and sells them at the rate of $5$ for $Rs. 12.$ Find his gain or loss percent.
Answer$CP$ of $1$ dozen or $12$ lemons $= Rs. 25$
$SP$ of $5$ lemons $= Rs. 12$
$\therefore\text{SP of 12 lemons}=\text{Rs. }\frac{12\times12}{5}$
$=\text{Rs. }\frac{144}{5}$
$=\text{Rs. }28.80$ Gain $= SP - CP$
$Rs. 28.80 - Rs. 25 = Rs. 3.80$
$\therefore\text{Gain}\%=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{3.80\times100}{25}=15.2\%$
$=15.2\%$
View full question & answer→Question 173 Marks
Find the $SP$ when:
$CP = Rs. 1540,$ loss $= 4\%$
Answer$C.P. = Rs. 1540$
Loss $= 4\%$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100-\text{Loss%})}{100}$
$=\frac{1540\times(100-4)}{100}$
$=\frac{1540\times96}{100}$
$=\text{Rs. }1478.40$
View full question & answer→Question 183 Marks
Find the $C.P.$ when: $SP = Rs. 8510,$ loss $= 8\%$
Answer$S.P. = Rs. 8510$ Gain$\%$
$8\%$
$\therefore\text{C.P.}=\frac{\text{S.P.}\times100}{100-\text{Loss%}}$
$=\frac{8510\times100}{100-8}$
$=\text{Rs. }\frac{8510\times100}{92}$
$=\text{Rs. }9250$
View full question & answer→Question 193 Marks
Find the gain or loss per cent when: $CP = Rs. 1800$ and $SP = Rs. 1611$
Answer$C.P. = Rs. 1800$
$SP = Rs. 1611$
$\therefore$ Loss $= SP - CP = 1800 - 1611 = Rs. 189$
$\therefore\text{Loss%}=\frac{\text{Total Loss}\times100}{\text{CP}}$
$=\frac{189\times100}{1800}$
$=\frac{21}{2}\%$
$=10.5\%$
View full question & answer→Question 203 Marks
Manoj purchased a video for $Rs. 12000.$ He sold it to Rahul at a gain of $10\%.$ If Rahul sells it to Rakesh at a loss of $5\%,$ what did Rakesh pay for it$?$
AnswerFor Manoj $CP$ of video $= Rs. 12000$ Gain $= 10\%$
$\therefore\text{SP of video}\%=\frac{\text{CP}\times(100+\text{gain%})}{100}$
$=\frac{12000\times(100+10)}{100}$
$=\text{Rs. }\frac{12000\times110}{100}$
$=\text{Rs. }13200$ Or
$CP$ for Rahul $= Rs. 13200$ Loss $= 5\%$
$\therefore\text{SP for Rahul}= \frac{13200\times(100-5)}{100}$
$=\text{Rs. }\frac{13200\times95}{100}$
$\text{Rs. }12540$
$\therefore CP$ for Rakesh $= Rs. 12540$
View full question & answer→Question 213 Marks
The selling price of $16$ spoons is equal to the cost price of $15$ spoons. Find the loss percent.
AnswerLet the cost price of one spoon be $Rs.1.$
$CP$ of $16$ spoons $= Rs. 16$
$SP$ of $16$ spoons $= CP$ of $15$
spoons $= Rs. 15$
Loss $= CP - SP = (16 - 15) = Re.1$
$\text{Loss}\%=\Big(\frac{\text{Loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{31}{16}\times100\Big)\%$
$=6.25\%$ Loss$\% = 6.25\%$
View full question & answer→Question 223 Marks
Find the $SP$ when: $CP = Rs. 8640,$ loss $=12\frac{1}{2}\%$
Answer$C.P. = Rs. 8640$ Loss $=12\frac{1}{2}=\frac{25}{2}\%5$
$\therefore\text{S.P.}=\frac{\text{C.P}\times(100-\text{Loss%})}{100}$
$=\text{Rs. }\frac{8640\times\Big(100-\frac{25}{2}\Big)}{100}$
$=\text{Rs. }\frac{8640\times175}{2\times100}$
$=\text{Rs. }7560$
View full question & answer→Question 233 Marks
Find the gain or loss per cent when:
$CP = Rs. 2400$ and $SP = Rs. 2592$
Answer$C.P. = Rs. 2400$
$SP = Rs. 2592$
Gain $= SP - CP$
$= Rs. 2592 - Rs. 2400 = Rs. 192$
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{192\times100}{2400}$
$=8\%$
View full question & answer→Question 243 Marks
If the manufacturer gains $10\%$ the wholesale dealer $15\%,$ and the retailer $25\%$ then what is the productions cost of a washing machine whose retail price is $Rs. 37950?$
AnswerRetail price or $S.P.$ of the machine for retailer $= Rs. 37950$
Gain = 25% $\therefore\text{CP for retailer}=\frac{\text{S.P.}\times100}{100+\text{gain}}$
$=\text{Rs. }\frac{37950\times100}{100+25}$
$=\text{Rs. }\frac{37950\times100}{125}$
$=\text{Rs. }30360$ Or $S.P.$ for wholesalar $= Rs. 30360$ Gain $15\%$
$\therefore C.P.$ for wholesalar $=\text{Rs. }\frac{30360\times100}{100+15}$
$=\text{Rs. }\frac{30360\times100}{115}$
$=\text{Rs. }26400$ Or $S.P.$ for manufacturer $= Rs. 26400$ Gain $= 10\%$
$\therefore C.P.$ for production $=\text{Rs. }\frac{26400\times100}{100 + 10}$
$=\text{Rs. }\frac{26400\times100}{110}$
$=\text{Rs. }24000$
View full question & answer→Question 253 Marks
Find the gain or loss per cent when: $CP = Rs. 12000$ and $SP = Rs. 12800$
Answer$C.P. = Rs. 12000$
$SP = Rs. 12800$
Gain $= SP - CP = Rs. 12800 - Rs. 12000 = Rs. 800$
$\therefore\text{Gain%}=\frac{\text{Total gain}\times100}{\text{CP}}$
$=\frac{800\times100}{12000}$
$=\frac{20}{3}\%$
$=6\frac{2}{3}\%$
View full question & answer→Question 263 Marks
On selling a fan for $Rs. 2585$ a man gains $\frac{1}{2}$ of its cost price. Find the cost price of the fan.
AnswerLet the cost price of the fan be $Rs. x.$
$\text{Gain}=\text{Rs. }\frac{\text{x}}{10}$
$SP$ of the fan $=\Big(\text{x}+\frac{\text{x}}{10}\Big)$
$=\text{Rs. }\frac{11}{10}\text{x}$
$SP$ of the fan $= Rs. 2585$
$\therefore\frac{11}{10}\text{x}=2585$
$\Rightarrow11\text{x}=25850$
$\Rightarrow\text{x}=\frac{25850}{11}=2350$
So, $CP$ of the fan is $Rs. 2350.$
View full question & answer→