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41 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
A trader marks his goods at 30% above cost price and allows a discount of 10%. What is his gain percent?
Answer
Let 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%.
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Question 23 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.
Answer
Cost 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
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Question 33 Marks
Find the selling price when.
CP = Rs. 645 and loss % $=13\frac{1}{3}\%$
Answer
CP = Rs. 645
Loss percentage $=13\frac{1}{3}\%=\frac{40}{3}\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100+\frac{40}{3}\big)}{10}\times645$
$=\frac{\big(\frac{300-40}{3}\big)}{100}\times645$
$=\big(\frac{260}{3}\big)\times\big(\frac{1}{100}\big)\times645$
$=\text{Rs. }559$
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Question 43 Marks
Find the cost price when.
SP = Rs. 657.60 and loss % = 4%
Answer
SP = Rs. 657.60
Loss percentage = 4%
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{(100+12)}\times657.60$
$=\text{Rs. }685$
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Question 53 Marks
Find the selling price when.
CP = Rs. 875 and loss % = 12%
Answer
CP = Rs. 875
Loss percentage = 12%
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100-12\big)}{10}\times875$
$=\frac{77000}{100}$
$=\text{Rs. }770$
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Question 63 Marks
Malti bought a VCR for Rs. 19980 including VAT. If the original price of VCR be Rs. 18500, find the rate of VAT.
Answer
Let 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%.
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Question 73 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 $=\frac{\text{Distance}}{\text{MP}}\times100\%=\frac{208}{1300}\times100\%=16\%$
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Question 83 Marks
By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss percent.
Answer
Let 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 $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{38\text{x}}{48\text{x}}\times100\Big)\%$
$=6\frac{1}{4}\%$
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Question 93 Marks
Find the cost price when.
SP = Rs. 1596 and gain % = 12%
Answer
SP = Rs. 1596
Gain percentage = 12%
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{(100+12)}\times1596$
$=\text{Rs. }1425$
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Question 113 Marks
Rajan bought a watch for Rs. 1870 including VAT at 10%. Find the original price of the watch.
Answer
Let 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.
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Question 123 Marks
Find the cost price when.
SP = Rs. 34.40 and gain % $=7\frac{1}{2}\%$
Answer
SP = Rs. 34.40
Loss percentage $=7\frac{1}{2}\%=\frac{15}{2}\%$
$\text{CP}=\frac{100}{(100+\text{gain}\%)}\times\text{SP}$
$=\frac{100}{\big(100+\frac{15}{2}\big)}\times34.40$
$=\frac{100\times2}{215}\times34.40$
$=\text{Rs. }32$
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Question 133 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 $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{3.2}{80}\times100\Big)\%$
$=\Big(\frac{32}{80}\Big)\%$
$=4\%$
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Question 143 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 $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{27.6}{345}\times100\Big)\%$
$=\Big(\frac{2760}{345}\Big)\%$
$=8\%$
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Question 153 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
  1. 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
  1. 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
  1. 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
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Question 163 Marks
After allowing a discount of 8% on a toy, it is sold for Rs. 216.20. Find the marked price of the toy.
Answer
Selling 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
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Question 173 Marks
Karuna bought 10g of gold for Rs. 15756 including VAT at 1%. What is the rate of gold per 10g?
Answer
Let 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
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Question 183 Marks
Mohit bought a shirt for Rs. 1337.50 including VAT at 7%. Find the original price of the shirt.
Answer
​​Let 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, $\frac{107\text{x}}{100}=1337.50$
$\Rightarrow\text{x}=\text{Rs. }\Big(1337.50\times\frac{100}{107}\Big)$
$=\text{Rs. }1250$
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Question 193 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.
Answer
Let 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%.
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Question 203 Marks
Find the selling price when.
CP = Rs. 915 and gain % $=6\frac{2}{3}\%$
Answer
CP = Rs. 915
Gain percentage $=6\frac{2}{3}\%=\frac{20}{3}\%$
$\text{SP}=\frac{(100+\text{gain}\%)}{100}\times\text{CP}$
$=\frac{\big(100+\frac{20}{3}\big)}{10}\times915$
$=\frac{\big(\frac{320}{3}\big)}{100}\times915$
$=\big(\frac{320}{3}\big)\times\big(\frac{1}{100}\big)\times915$
$=\text{Rs. }976$
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Question 213 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.
Answer
Let 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.
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Question 223 Marks
If the selling price of a flower vase is $\frac{5}{6}$ of its cost price, find the loss percent.
Answer
Let 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 $=\text{x}-\frac{5}{6}\text{x}=\text{Rs. }\frac{\text{x}}{6}$
$\text{Loss} \% =\frac{\text{loss}}{\text{CP}}\times100\%=\frac{\frac{\text{x}}{6}}{\text{x}}\times100\%$
$=\frac{100}{6}\%=\frac{50}{3}\%=16\frac{2}{3}\%$
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Question 233 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.
Answer
Marked 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
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Question 243 Marks
Hari bought 20kg of rice at Rs. 36/kg and 25kg 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.
Answer
Total 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 $=\frac{\text{gain}}{\text{CP}}\times100\%=\frac{190}{1520}\times100\%=12\frac{1}{2}\%$
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Question 253 Marks
Find the single discount which is equivalent to two successive discounts of 20% and 5%.
Answer
​Let 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%
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Question 263 Marks
If the cost price of 12 pens is equal to the selling price of 16 pens, find the loss percent.
Answer
Let 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
$\therefore\text{Loss percentage}=\frac{\text{loss}}{\text{CP}}\times100$
$=\frac{4\text{x}}{16\text{x}}\times100$
$=25\%$
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Question 273 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.
Answer
Let 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
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Question 283 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 $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{45}{675}\times100\Big)\%$
$=6\frac{2}{3}\%$
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Question 293 Marks
Sajal purchased some car parts for Rs. 20776 including VAT at 12%. What is the original cost of these spare parts?
Answer
​Let 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
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Question 303 Marks
Tanvy bought a watch for Rs. 1980 including VAT at 10%. Find the original price of the watch.
Answer
Let 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
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Question 313 Marks
Find the single discount equivalent to two successive discounts of 20% and 10%.
Answer
Let 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%.
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Question 323 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\%$
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Question 333 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$
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Question 343 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$
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Question 353 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.
Answer
Let 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%.
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Question 363 Marks
The list price of a refrigerator is Rs. 14650. If 6% is charged as sales tax, find the cost of the refrigerator.
Answer
List 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
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Question 373 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}\%$
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Question 383 Marks
If the selling price of a TV set is equal to $\frac{6}{5}$ of its cost price, find the gain percent.
Answer
Let 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\%$
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Question 393 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.
Answer
Marked 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%.
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Question 403 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?
Answer
​Let 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.
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Question 413 Marks
Mohini purchased a computer for Rs. 37960 including VAT at 4%. What is the original price of the computer?
Answer
Let 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
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