Question 12 Marks
A trader marks his goods at $30\%$ above cost price and allows a discount of $10\%$. What is his gain percent$?$
AnswerLet the $CP$ be $Rs. 100.$
Then, marked price $= Rs. 130$
Discount $= 10\%$ of $MP = (10\%$ of $Rs. 130)$
$=\text{Rs. }\Big(130\times\frac{10}{100}\Big)$
$=\text{Rs. }13$ Now, $SP = (MP) - ($discount$) =Rs. (130 - 13) = Rs. 117$
$\therefore$ Gain percentage $= (117 - 100)\% = 17\%$
$\therefore$ The gain percentage of the trader is $17\%.$
View full question & answer→Question 22 Marks
A tea set was bought for $Rs. 528$ after getting a discount of $12\%$ on its marked price. Find the marked price of the tea set.
AnswerCost price $= Rs. 528$ Rate of discount
$= 12\%$ Marked price $= ?$
$SP = MP\ -\ $discount Let the $MP$ be $Rs. x$
Now, $\frac{\text{x}-12}{100\times\text{x}}=528$
$\Rightarrow\frac{88\text{x}}{100}=528$
$\Rightarrow88\text{x}=52800$
$\Rightarrow\text{x}=\frac{52800}{88}$
$\Rightarrow\text{x}=600$
Therefore, the marked price of tea set is $= Rs. 600$
View full question & answer→Question 32 Marks
Find the selling price when. $CP = Rs. 645$ and loss % $=13\frac{1}{3}\%$
Answer$CP = Rs. 645$ Loss percentage $=13\frac{1}{3}\%=\frac{40}{3}\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100+\frac{40}{3}\big)}{10}\times645$
$=\frac{\big(\frac{300-40}{3}\big)}{100}\times645$
$=\big(\frac{260}{3}\big)\times\big(\frac{1}{100}\big)\times645$
$=\text{Rs. }559$
View full question & answer→Question 42 Marks
Find the cost price when. $SP = Rs. 657.60$ and loss $\% = 4\%$
Answer$SP = Rs. 657.60$
Loss percentage $= 4\%$
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{(100+12)}\times657.60$
$=\text{Rs. }685$
View full question & answer→Question 52 Marks
Find the selling price when. $CP = Rs. 875$ and loss $\% = 12\%$
Answer$CP = Rs. 875$
Loss percentage $= 12\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100-12\big)}{10}\times875$
$=\frac{77000}{100}$
$=\text{Rs. }770$
View full question & answer→Question 62 Marks
Malti bought a $VCR$ for $Rs. 19980$ including $VAT.$ If the original price of $VCR$ be $Rs. 18500,$ find the rate of $VAT.$
AnswerLet the rate of $VAT$ be $x \%.$
Then, We have: $18500 + x \%$ of $18500 = 19980$
$\Rightarrow\Big(\frac{\text{x}}{100}\times18500\Big)=19980-18500$
$\Rightarrow185\text{x}=1480$
$\Rightarrow\frac{1480}{185}=8$
$\therefore$ The rate of $VAT$ is $8\%.$
View full question & answer→Question 72 Marks
Find the rate of discount being given on a shirt whose selling price is $Rs. 1092$ after deducting a discount of $Rs. 208$ on its marked price.
Answer$SP$ of the shirt $= Rs. 1,092$
Discount $= Rs. 208$
$MP = SP\ +$ Discount $= Rs. 1,092 + Rs. 208 = Rs. 1,300$
$\therefore$ Rate of discount $=\frac{\text{Distance}}{\text{MP}}\times100\%=\frac{208}{1300}\times100\%=16\%$
View full question & answer→Question 82 Marks
By selling $45$ lemons, a vendor loses a sum equal to the selling price of $3$ lemons. Find his loss percent.
AnswerLet $Rs. x$ be the $SP$ of one lemon.
$SP$ of $45$ lemons $= Rs. 45x$
Loss $= SP$ of $3$ lemons $= Rs. 3x$
But loss $= CP - SP$
$CP = loss + SP$
$= 3x + 45x$
$= Rs. 48x$
$\therefore$ Loss percentage $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{38\text{x}}{48\text{x}}\times100\Big)\%$
$=6\frac{1}{4}\%$
View full question & answer→Question 92 Marks
Find the cost price when. $SP = Rs. 1596$ and gain $\% = 12\%$
Answer$SP = Rs. 1596$
Gain percentage $= 12\%$
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{(100+12)}\times1596$
$=\text{Rs. }1425$
View full question & answer→Question 102 Marks
By selling a flower pot for $Rs. 322,$ a man gains $15\%.$ At what price should he sell it to gain $20\%?$
Answer$SP = Rs. 322$ Gain percentage $= 15\%$
$\therefore\text{CP}=\Big\{\frac{100}{(100+\text{gain}\%)}\times\text{SP}\Big\}$
$=\text{Rs. }\Big\{\frac{100}{(100+15)}\times322\Big\}$
$=\text{Rs. }\Big(\frac{100}{115}\times322\Big)$
$=\text{Rs. }280$ Now, $\text{desired SP}=\Big\{\frac{(100+\text{gain}\%)}{100}\times\text{CP}\Big\}$
$=\text{Rs. }\Big\{\frac{100+20}{100}\times280\Big\}$
$=\text{Rs. }\Big(\frac{120}{100}\times280\Big)$
$=\text{Rs. }336$
$\therefore$ The desired selling price is $Rs. 336.$
View full question & answer→Question 112 Marks
Rajan bought a watch for $Rs. 1870$ including $VAT$ at $10\%$. Find the original price of the watch.
AnswerLet the original price be $Rs. x. VAT = 10\%$ of $Rs. x$
$=\text{Rs. }\Big(\text{x}\times\frac{10}{100}\Big)$
$=\text{Rs. }\frac{\text{x}}{10}$
$\therefore$ Price including $VAT =\text{Rs. }\Big(\text{x}+\frac{\text{x}}{10}\Big)$
$=\text{Rs. }\frac{11\text{x}}{10}$
$\therefore\frac{11\text{x}}{10}=1870$
$\Rightarrow\text{x}=\Big(1870\times\frac{10}{11}\Big)$
$\Rightarrow\text{x}=1700$
$\therefore$ The original price of the watch is $Rs. 1,700.$
View full question & answer→Question 122 Marks
Find the cost price when. $SP = Rs. 34.40$ and gain $\%$ $=7\frac{1}{2}\%$
Answer$SP = Rs. 34.40$
Loss percentage $=7\frac{1}{2}\%=\frac{15}{2}\%$
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{\big(100+\frac{15}{2}\big)}\times34.40$
$=\frac{100\times2}{215}\times34.40$
$=\text{Rs. }32$
View full question & answer→Question 132 Marks
Find the gain or loss percent when.
$CP = Rs. 80$ and $SP = Rs. 76.80$
Answer$CP = Rs. 80$
$SP = Rs. 76.80$
Since $SP > CP,$ there is a loss
Loss $= 80 - 76.80 = Rs. 3.2$
Loss percentage $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{3.2}{80}\times100\Big)\%$
$=\Big(\frac{32}{80}\Big)\%$
$=4\%$
View full question & answer→Question 142 Marks
Find the gain or loss percent when. $CP = Rs. 345$ and $SP = Rs. 372.60$
Answer$CP = Rs. 345$
$SP = Rs. 372.60$
Since $SP > CP,$ there is a gain Gain $= 675 - 630 = Rs. 45$
Gain percentage $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{27.6}{345}\times100\Big)\%$
$=\Big(\frac{2760}{345}\Big)\%$
$=8\%$
View full question & answer→Question 152 Marks
Reena bought the following articles from a general store.
$1.\ 1$ tie costing $Rs. 250$ with $ST\ @ 6\%$
$2.$ Medicines costing $Rs. 625$ with $ST\ @ 4\%$
$3.$ Cosmetics costing $Rs. 430$ with $ST\ @ 10\%$
$4.$ Clothes costing $Rs 1175$ with $ST\ @ 8\%$ Calculate the total amount to be paid by Reena.
Answer$1.$ Cost of the tie $= Rs. 250$
Sales tax $= 6\%$ of $Rs. 250$
$=\text{Rs. }(250\times\frac{6}{100})=\text{Rs. }15$
Hence, bill amount $= Rs. (250 + 15) = Rs. 265$
$2.$ Cost of the medicines $= Rs. 625$
Sales tax $= 4\%$ of $Rs. 625$
$=\text{Rs. }(625\times\frac{4}{100})=\text{Rs. }25$
Hence, bill amount $= Rs. (625 + 25) = Rs. 650$
$3.$ Cost of the cosmetics $= Rs. 430$
Sales tax $= 10\%$ of $Rs. 430$
$=\text{Rs. }(430\times\frac{10}{100})=\text{Rs. }43$
Hence, bill amount $= Rs. (430 + 43) = Rs. 473$
$4.$ Cost of clothes $= Rs. 1175$
Sales tax $= 8\%$ of $Rs. 1175$
$=\text{Rs. }(1175\times\frac{8}{100})=\text{Rs. }93$
Hence, bill amount $= Rs. (1175 + 94) = Rs. 1269$
Therefore, total amount to be paid by Reena $=$ bill amount of all the four items.
$= Rs. (265 + 650 + 473 + 1269) = Rs. 2657$
View full question & answer→Question 162 Marks
After allowing a discount of $8\%$ on a toy, it is sold for $Rs. 216.20.$ Find the marked price of the toy.
AnswerSelling Price $= Rs. 216.20$
Rate of discount $= 8\%$
Marked Price $= ?$
$SP = MP\ -$ discount
Let the $MP$ be $Rs. x$
Now, $\text{x}-\frac{8}{100}\times\text{x}=216.20$
$\Rightarrow\frac{92\text{x}}{100}=216.20$
$\Rightarrow92\text{x}=21620$
$\Rightarrow\text{x}=\frac{21620}{92}$
$\Rightarrow\text{x}=235$
$\therefore$ Marked price $= Rs. 235$
View full question & answer→Question 172 Marks
Karuna bought $10g$ of gold for $Rs. 15756$ including $VAT$ at $1\%.$ What is the rate of gold per $10g?$
AnswerLet the price of $10g$ of gold be $Rs. x$
$VAT = 1\%$ of $Rs. x$ $=\text{Rs. }\Big(\text{x}\times\frac{1}{100}\Big)$
$=\text{Rs. }\frac{\text{x}}{100}$
$\therefore$ Price including $VAT=\text{Rs. }\Big(\text{x}+\frac{\text{x}}{100}\Big)$
$=\text{Rs. }\frac{101\text{x}}{100}$ Now, $\frac{101\text{x}}{100}=15756$
$\Rightarrow\text{x}=\text{Rs. }\Big(15756\times\frac{100}{101}\Big)$
$=\text{Rs. }15600$ Hence, the price of $10g$ of gold is $Rs. 15,600$
View full question & answer→Question 182 Marks
Mohit bought a shirt for $Rs. 1337$. $50$ including $VAT$ at $7\%.$ Find the original price of the shirt.
AnswerLet the original price of the shirt be $Rs. xVAT = 7\%$ of $Rs. x$
$=\text{Rs. }\Big(\text{x}\times\frac{7}{100}\Big)$
$=\text{Rs. }\frac{7\text{x}}{100}$
$\therefore$ Price including $VAT =\text{Rs. }\Big(\text{x}\times\frac{7\text{x}}{100}\Big)$
$=\text{Rs. }\frac{107\text{x}}{100}$
Now, $\frac{107\text{x}}{100}=1337.50$
$\Rightarrow\text{x}=\text{Rs. }\Big(1337.50\times\frac{100}{107}\Big)$
$=\text{Rs. }1250$
View full question & answer→Question 192 Marks
The value of a car including VAT is Rs. 382500. If the basic price of the car be Rs. 340000, find the rate of VAT on cars.
AnswerLet the rate of VAT be x %. Then, We have: 34000 + x % of 34000 = 380 $\Rightarrow\Big(\frac{\text{x}}{100}\times340000\Big)=382500-340000$ $\Rightarrow3400\text{x}=42500$ $\Rightarrow\text{x}=\frac{42500}{3400}=12.5$ $\therefore$ The rate of VAT is 12.5%.
View full question & answer→Question 202 Marks
Find the selling price when. $CP = Rs. 915$ and gain $\%=6\frac{2}{3}\%$
Answer$CP = Rs. 915$ Gain percentage $=6\frac{2}{3}\%=\frac{20}{3}\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100+\frac{20}{3}\big)}{10}\times915$
$=\frac{\big(\frac{320}{3}\big)}{100}\times915$
$=\big(\frac{320}{3}\big)\times\big(\frac{1}{100}\big)\times915$
$=\text{Rs. }976$
View full question & answer→Question 212 Marks
A dealer gets $Rs. 30$ less if instead of selling a chair at a gain of $12\%$ he sells it at a gain of $8\%.$ Find the cost price of the chair.
AnswerLet the $CP$ be $Rs. x.$
Then, we have: $(12\%$ of $x) - (8\%$ of $x) = 30$
$\Rightarrow\Big(\text{x}\times\frac{12}{100}\Big)-\Big(\text{x}\times\frac{8}{100}\Big)=30$
$\Rightarrow\Big(\frac{12\text{x}}{100}-\frac{8\text{x}}{100}\Big)=30$
$\Rightarrow\frac{4\text{x}}{100}=30$
$\Rightarrow\text{x}=\Big(30\times\frac{100}{4}\Big)$
$=750$
$\therefore$ The cost price of the chair is $Rs. 750.$
View full question & answer→Question 222 Marks
If the selling price of a flower vase is $\frac{5}{6}$ of its cost price, find the loss percent.
AnswerLet the $CP$ of the flower vase be $Rs. x$
$SP$ of the flower vase $=\frac{5}{6}\text{CP}=\text{Rs. }\frac{5}{6}\text{x}$ Loss = $CP - SP$
$=\text{x}-\frac{5}{6}\text{x}=\text{Rs. }\frac{\text{x}}{6}$
$\text{Loss} \% =\frac{\text{loss}}{\text{CP}}\times100\%=\frac{\frac{\text{x}}{6}}{\text{x}}\times100\%$
$=\frac{100}{6}\%=\frac{50}{3}\%=16\frac{2}{3}\%$
View full question & answer→Question 232 Marks
The marked price of a water cooler is $Rs. 4650.$ The shopkeeper offers an off-season discount of $18\%$ on it. Find its selling price.
AnswerMarked price $= Rs. 4650$ and discount $= 18\%$
Discount $= 18\%$ of marked price $= 18\%$ of $Rs. 4650$
$=\text{Rs .}\Big(4650\times\frac{18}{100}\Big)\text{Rs. }837$
Selling price $=$ marked price $-$ discount $Rs. (4650 - 837) = Rs. 3813$
Therefore, the selling price of the cooler is $Rs. 3813$
View full question & answer→Question 242 Marks
Hari bought $20\ kg$ of rice at $Rs. 36/kg$ and $25\ kg$ of rice at $Rs. 32/kg$ He mixed the two varieties and sold the mixture at $Rs. 38/kg$ Find his gain percent in the whole transaction.
AnswerTotal cost of rice of $1st$ variety $= Rs. 36/kg × 20kg = Rs. 720$
Total cost of rice of $2nd$ variety $= Rs. 32/kg × 25kg = Rs. 800$
Total cost of the two rice varieties $= Rs. 720 + Rs. 800 = Rs. 1,520$
Total quantity of the two rice varieties $= 20kg + 25kg = 45kg$
Selling price of the mixture of two rice $= Rs. 38/kg × 45kg = Rs. 1,710$
Gain $= Sp - CP = Rs. 1,710 - Rs. 1,520 = Rs. 190$
Gain $=\frac{\text{gain}}{\text{CP}}\times100\%=\frac{190}{1520}\times100\%=12\frac{1}{2}\%$
View full question & answer→Question 252 Marks
Find the single discount which is equivalent to two successive discounts of $20\%$ and $5\%.$
AnswerLet the marked price of the article be $Rs. 100.$
First discount $= 20\%$
Price after the first discount $= (100 - 20) = Rs. 80$
Second discount $= 5\%$ of $80 =\frac{5}{100}\times80=\text{ Rs. }4$
Price after the second discount $= (80 - 4) = Rs. 76$
Net selling price $= Rs. 76$
$\therefore$ Single discount equivalent to the given successive discounts $= (100 - 76)\% = 24\%$
View full question & answer→Question 262 Marks
If the cost price of $12$ pens is equal to the selling price of $16$ pens, find the loss percent.
AnswerLet the $CP$ of each pen be $Rs. x.$
$CP$ of $16$ pens $= Rs. 16x$
$SP$ of $16$ pens $= CP$ of $12$ pens $= Rs. 12x$
i.e., $CP > SP$ Now, loss $= CP − SP = (16x − 12x) = Rs. 4x$
$\therefore\text{Loss percentage}=\frac{\text{loss}}{\text{CP}}\times100$
$=\frac{4\text{x}}{16\text{x}}\times100$ $=25\%$
View full question & answer→Question 272 Marks
A cycle was sold at a gain of $10\%.$ Had it been sold for $Rs. 260$ more, the gain would have been $14\%.$ Find the cost price of the cycle.
AnswerLet the $CP$ be $Rs. x. $
$SP$ when gain is $10\% =\text{x}+\frac{10}{100}\text{x}=\text{Rs. }\frac{110}{100}\text{x}$
$SP$ when gain is $14\% =\text{x}+\frac{10}{100}\text{x}=\text{Rs. }\frac{110}{100}\text{x}$
Difference in $SP = SP$ when gain is $14\% - SP$ when gain is $10\% = Rs. 260$
$\therefore\frac{114\text{x}}{100}-\frac{110\text{x}}{100}=260$
$\Rightarrow\frac{4\text{x}}{100}=260$
$\Rightarrow\text{x}=6500$
Hence, the $CP$ of the cycle is $Rs. 6,500$
View full question & answer→Question 282 Marks
Find the gain or loss percent when. CP = Rs. 675 and $SP = Rs. 630$
Answer$CP = Rs. 675$
$SP = Rs. 630$ Since $SP > CP,$
there is a loss Loss $= 675 - 630 = Rs. 45$
Loss percentage $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{45}{675}\times100\Big)\%$
$=6\frac{2}{3}\%$
View full question & answer→Question 292 Marks
Sajal purchased some car parts for $Rs. 20776$ including $VAT$ at $12\%$. What is the original cost of these spare parts$?$
AnswerLet the original cost of the spare parts be $Rs. xVAT = 12\%$ of $Rs. x$
$=\text{Rs. }\Big(\text{x}\times\frac{12}{100}\Big)$
$=\text{Rs. }\frac{12\text{x}}{100}$$\therefore$ Price including $VAT$
$=\text{Rs. }\Big(\text{x}\times\frac{12\text{x}}{100}\Big)$
$=\text{Rs. }\frac{112\text{x}}{100}$ Now, $\frac{112\text{x}}{100}=20776$
$\Rightarrow\text{x}=\text{Rs. }\Big(20776\times\frac{100}{112}\Big)$
$=\text{Rs. }18550$ Hence, the original cost of the spare parts is $Rs. 18,550$
View full question & answer→Question 302 Marks
Tanvy bought a watch for $Rs. 1980$ including $VAT$ at $10\%.$ Find the original price of the watch.
AnswerLet the original price of the watch be $Rs. x$
$VAT = 10\%$ of $Rs. x$
$=\text{Rs. }\Big(\text{x}\times\frac{10}{100}\Big)$
$=\text{Rs. }\frac{10\text{x}}{100}$
$\therefore$ Price including VAT $=\text{Rs. }\Big(\text{x}+\frac{\text{x}}{100}\Big)$
$=\text{Rs. }\frac{11\text{x}}{100}$
Now, $=\frac{11\text{x}}{100}=1980$
$\Rightarrow\text{x}=\Big(1980\times\frac{10}{11}\Big)=1800$
Hence, the original price of the watch is $Rs. 1,800$
View full question & answer→Question 312 Marks
Find the single discount equivalent to two successive discounts of $20\%$ and $10\%.$
AnswerLet the marked price be $Rs. 100.$
Then, first discount on it $= Rs. 20$
Price after the first discount $= Rs. (100 - 20)$
$= Rs. 80$
Second discount on it $= 10\%$ of $Rs. 80$
$=\text{Rs. }\Big(80\times\frac{10}{100}\Big)$
$= Rs. 8$
Price after the second discount $= Rs. (80 - 8)$
$= Rs. 72$
Net selling price $= Rs. 72$
Single discount equivalent to given successive discounts $= (100 - 72)\%$
$= 28\%$
The single discount equivalent to given successive discounts is $28\%.$
View full question & answer→Question 322 Marks
Find the gain or loss percent when. $CP = Rs. 620$ and $SP = Rs. 713$
Answer$CP = Rs. 620$
$SP = Rs. 713$ Since $SP > CP,$ there is a gain Gain $= 713 - 620 = Rs. 93$ Gain percentage $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{93}{620}\times100\Big)\%$
$=15\%$
View full question & answer→Question 332 Marks
Find the cost price when. $SP = Rs. 2431$ and loss $\%=6\frac{1}{2}\%$
Answer$SP = Rs. 2431$
Loss percentage $=6\frac{1}{2}\%=\frac{13}{2}\%$
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{\big(100-\frac{13}{2}\big)}\times2431$
$=\frac{100\times2}{187}\times2431$
$=\text{Rs. }2600$
View full question & answer→Question 342 Marks
Find the selling price when. $CP = Rs. 1650$ and gain $\% = 4\%$
Answer$CP = Rs. 1650$ Gain percentage $= 4\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{(104\times4)}{100}\times1650$
$=\frac{104\times1650}{100}$
$=\text{Rs. }1716$
View full question & answer→Question 352 Marks
Rohit purchased a pair of shoes for $Rs. 882$ inclusive of $VAT.$ If the original cost be $Rs. 840$, find the rate of $VAT.$
AnswerLet the rate of $VAT$ be $x \%.$ Then, we have $840 + x \%$ of $840 = 882$
$\Rightarrow\Big(\frac{\text{x}}{100}\times840\Big)=882-840$
$\Rightarrow\frac{84\text{x}}{10}=42$
$\Rightarrow\text{x}=\Big(42\times\frac{10}{84}\Big)=5$
$\therefore$ The rate of $VAT$ is $5\%.$
View full question & answer→Question 362 Marks
The list price of a refrigerator is $Rs. 14650$. If $6\%$ is charged as sales tax, find the cost of the refrigerator.
AnswerList price of the refrigerator $= Rs. 14650$
Sales tax $= 6\%$ of $Rs. 14650$
$=\text{Rs. }\Big(14650\times\frac{6}{100}\Big)$
$=\text{Rs. }879$ Bill amount $=\text{Rs. }(14650+879)$
$=\text{Rs. }15529$
Hence, the cost of the refrigerator is $Rs. 15,529$
View full question & answer→Question 372 Marks
Robin purchased an old car for $Rs. 73500.$ He spent $Rs. 10300$ on repairs and paid $Rs. 2600$ for its insurance. Then he sold it to a mechanic for $Rs. 84240.$ What was his percentage gain or loss$?$
Answer$CP$ of the car $= Rs. 73500$
Repairs $= Rs. 10300$
Insurance $= Rs. 2600$
Total $CP = 73500 + 10300 + 2600 = Rs.86400$
$SP = Rs. 84240$
Since $SP < CP,$ Robin has a loss.
Loss $= 86400 - 84240 = Rs. 2160$
Loss percentage $=\Big(\frac{\text{loss}}{\text{total CP}}\times100\Big)\%$
$=\Big(\frac{2160}{86400}\times100\Big)\%$
$=2\frac{1}{2}\%$
View full question & answer→Question 382 Marks
If the selling price of a $TV$ set is equal to $\frac{6}{5}$ of its cost price, find the gain percent.
AnswerLet the $CP$ of the $TV$ set be $Rs. x$
$SP$ of the $TV$ set $=\frac{6}{5}\text{CP}=\text{Rs. }\frac{6}{5}\text{x}$
Gain $= SP$ of the $TV$ set $-\ CP$ of the $TV$ set $=\frac{6}{5}\text{x}-\text{x}=\text{Rs. }\frac{\text{x}}{5}$
Gain $\% =\frac{\text{gain}}{\text{CP}}\times100\%=\frac{\frac{\text{x}}{5}}{\text{x}}\times100\%=\frac{100}{5}\%=20\%$
View full question & answer→Question 392 Marks
The price of a sweater was slashed from $Rs. 960$ to $Rs. 816$ by a shopkeeper in the winter season. Find the rate of discount given by him.
AnswerMarked Price $= Rs. 960$
Selling Price $= Rs. 816$
Discount $= MP - SP = Rs. (960 - 816) = Rs. 144$
Rate of discount $=144\times\frac{100}{960}=15\%$
Therefore, the discount on the sweater is $15\%.$
View full question & answer→Question 402 Marks
The sale price of a $TV$ set including $VAT$ is Rs. $27000$. If the $VAT$ is charged at $8\%$ of the list price, what is the list price of the $TV$ set?
AnswerLet the list price of the $TV$ set be Rs. $xVAT = 8\% $of Rs. $x$
$=\text{Rs. }\Big(\text{x}\times\frac{8}{100}\Big)$
$=\text{Rs. }\frac{8\text{x}}{100}$
$\therefore$ Price including $VAT =\text{Rs. }\Big(\text{x}\times\frac{8\text{x}}{100}\Big)$
$=\text{Rs. }\frac{108\text{x}}{100}$
Now, $\frac{108\text{x}}{100}=27000$
$\Rightarrow\text{x}=\text{Rs. }\Big(27000\times\frac{100}{108}\Big)$
$=\text{Rs. }25000$ Hence, the list price of the $TV$ set is Rs. $25,000.$
View full question & answer→Question 412 Marks
Mohini purchased a computer for Rs. $37960$ including $VAT$ at $4\%.$ What is the original price of the computer?
AnswerLet the original price of the computer be Rs. $x VAT = 4\%$ of Rs. x $=\text{Rs. }\Big(\text{x}\times\frac{4}{100}\Big)$
$=\text{Rs. }\frac{\text{4x}}{100}$
$\therefore$ Price including VAT $=\text{Rs. }\Big(\text{x}+\frac{\text{4x}}{100}\Big)$
$=\text{Rs. }\frac{104\text{x}}{100}$
Now, $\frac{104\text{x}}{100}=37960$
$\Rightarrow\text{x}=\text{Rs. }\Big(37960\times\frac{100}{104}\Big)$
$=\text{Rs. }36500$$\therefore$
The original price of the computer is Rs. $36,500$
View full question & answer→