Profit and loss
Amrit bought an article for Rs. 2,200 and sold it for Rs. 2,500. Here, his selling price is greater than the cost price. Hence, he got a profit of Rs. 2,500  Rs. 2,200 = Rs. 300. If he had sold the article for Rs. 2000, he would have a loss of Rs. 2,200  Rs. 2,000 = Rs. 200. The price for which an article is bought is known as the cost price (C.P.). The price for which it is sold is known as selling price (S.P.). If the selling price is greater than cost price, there is profit or gain. On the other hand, if the selling price is less than the cost price, there is a loss.
So, Profit = Selling price (S.P)  Cost price (C.P)
P = SP  CP and Loss =Cost price (C.P) Selling price (S.P)
L = CP  SP
The percentage profit or loss can be calculated using the following formula.
Actual profit = profit% of cost price
\(\text {Profit percentage} = \frac {Profit} {C.P}\times 100\)
Actual loss = loss% of Cost price.
\(\text {Loss percentage} = \frac {Loss} {C.P}\times 100\)
If S.P and profit or loss percent are given then
\(C.P = \frac {S.P \times 100} {100 + P\%} \: {or}\: C.P = \frac {S.P \times 100} {100  L\%}\)
If C.P. and profit or loss percentage are given then
\(S.P = \frac {C.P \times (100 + P\%)} {100}\: {or}\: S.P = \frac {C.P \times (100  L\%)} {100}\)
Discount
The seller may deduct a certain amount from the price of goods. The deduction is known as discount. The price from which the discount is deducted is called the marked price or labeled price. The price obtained by deducting the discount from marked price is called selling price
i.e. Selling price (S.P) = Market price (M.P)  Discount
S.P = M.P  D
or, M.P = S.P + D
or, D = M.P  S.P
If there is no discount, selling price = marked price [ S.P = M.P ]
\(\text {Discount percentage} = \frac {Discount} {M.P} ×100%\)
Value Added Tax (VAT)
Value Added Tax is a tax imposed by the government based on goods and services in each step of production and distribution. VAT is levied in the amount after allowing the discount (if there is) from the market price. In general, VAT is expressed in terms percentage which is called the rate of the VAT and it is fixed by the government. The cost of goods is determined by adding the VAT.
S.P = Orginal cost + VAT
\(\text {Rate of VAT} = \frac {VAT \;Amount} {Cost \; after \; discount (S.P)} \times 100\%\)
VAT amount = Rate of VAT (in%) \(\times\) discounted price.
 Profit or Gain = Selling Price  Cost Price
P = S.P  C.P  Profit percentage = \(\frac {Profit}{C.P} \times 100 \)
 Loss = Cost price  Selling Price
L = C.P  S.P  Loss percentage = \(\frac {Loss}{C.P} \times 100 \)
 Cost of goods or selling price = original cost + VAT
 Rate of VAT = \(\frac{VAT\; amount}{cost\; after\; discount\; (S.P)}\) \(\times\) 100%
 Vat Amount = Rate of VAT \(\times\) Discount price.
 The cost price of an article is constant.
 VAT is levied on discounted price.
Solution:
Profit% = 12 %
Profit = Rs 60
Selling price (SP) =?
If profit Rs 12 then SP is Rs 112
If profit Rs 1 then SP is Rs \(\frac{112}{12}\)
If profit Rs 60 then SP is \(\frac{112}{12} \times 60 = Rs \: 560\)
\(\therefore SP\) = Rs 560_{Ans.}
Solution:
Cost price (CP) = Rs 4500
Profit % (P) = 30%
Selling price (SP) =?
\begin{align*} SP &= \left( \frac{100 + P%}{100} \right) \times CP \\ &= \frac{100 + 30}{100} \times 4500 \\ &= \frac{4500 \times 130}{100}\\ &= Rs \: 5850\end{align*}
\(\therefore SP\) = 5850_{Ans.}
Solution:
Cost price (CP) = Rs 3405.50
Gain (G) = Rs 120
Selling price (SP) = ?
We know that,
\begin{align*} SP &= CP + profit \\ &= Rs 3405.0 + Rs 120 \\ &= Rs 3525.50_{ANS.} \end{align*}
Solution:
Cost price (CP) = Rs 220,000 + Rs 83500 = Rs 303,500
Selling price (SP) = Rs 300,000
Loss% =?
\begin{align*} Loss\% &= \frac {CP SP} {CP} \times 100\% \\ &= \frac{303,500  300,000}{303500} \times 100\% \\ &= 1.15\% \end{align*}
\(\therefore \) Loss = 1.15%_{Ans.}
Solution:
Selling price (SP) = Rs 2700
Loss% = 10%
\begin{align*} Cost \: price (CP) &= \frac{SP \times 100}{100  L\%} \\ &= \frac {2700 \times 100}{100  10 }\\ &= \frac{270000}{90} \\ &= Rs \: 3000 \end{align*}
Again,
CP = Rs 3000
Profit % = 7.5%
SP = ?
\begin{align*} SP &= \frac{1100 + P\%}{100 } \times CP \\ &= \frac{100 + 7.5\times 3000}{100}\\ &= Rs \: 3225 \end{align*}
\( \therefore \) selling price = 3325_{Ans}
Solution:
The price of doll before discount = Rs 180
The price of doll after discount = Rs 160
Amount of discount = Rs 180  Rs 160 = Rs 20
\begin{align*} Discount \% &= \frac{Amount \: of \: discount }{Initial \: price} \times 100\% \\ &= \frac{20}{180} \times 100\% \\ &= 11.11\% _{Ans.} \end{align*}
Solution:
Selling price (SP) = Rs. 164
Loss = 18%
\begin{align*} Cost \: price (C.P.) &= \frac{S.P. \times 100}{100  Loss \%} \\ &= \frac{164 \times 100}{100  18}\\ &= \frac{16400}{82}\\ &= Rs. 200 _{Ans}\end{align*}
Solution:
Market price (MP) = Rs. 1000
Discount % = 10%
\begin{align*}Payment\: amount &= MP  discount\% of MP \\ &= Rs. \: 1000  \frac{10}{100}\times 1000\\ &= Rs. 1000  Rs. 100 \\ &= Rs. 900_{Ans} \end{align*}
Solution:
Marked price (MP) = Rs. 150
Selling price after discount (SP) = Rs. 130
\begin{align*} Discount\% &= \frac{MP  SP}{MP} \times 100\% \\&= \frac {150  130}{150} \times 100\% \\ &= 13\frac{1}{3} \% \: \: _{Ans}\end{align*}
Solution:
Marked price (P) = Rs 2700
VAT = 13%
\begin{align*} Selling \: price \: (SP) &= MP + VAT\% of MP\\ &= 2700 + \frac{13}{100} \times 2700 \\ &= 2700 + 351 \\ &= Rs. \: 3051 \: \: \: _{Ans.} \end{align*}
Solution:
Let, cost price of calculator (CP_{1}) = Rs x
Cost price of the watch (CP_{2}) = RS (4000  x)
\begin{align*} SP \: of \: calculator \: (SP_1) &= CP + profit \\ &= x + x \: of \: 10\% \\ &= x + x \times \frac{10}{100}\\ &= \frac{11x}{10}\end{align*}
\begin{align*}SP \: of\: watch \: (SP_2) &=CP  loss\\ &= (4000  x) 20\% \: of \: (4000 + x)\\ &= (4000 x)  \frac{20}{100} \times (4000  x)\\ &=\frac{32000  5x 4000 + x}{5}\\ &= 3200  \frac{4x}{5} \end{align*}
\begin{align*} Total \: SP &= SP_1 + SP_2 \\ &= \frac{11x}{10} + 3200  \frac{4x}{5}\\ &= \frac{3x}{10} + 3200 \end{align*}
Total CP = 4000
Profit = 1%
\begin{align*}SP &= CP + Profit\\ or, \frac{3x}{10} + 3200 &= 4000 + 1\% of 4000\\ or, \frac{3x}{10} + 3200 &= 4000 + \frac{1}{100} \times 4000\\ or, \frac{3x}{10} &= 4000 + 40  3200\\ x &= 840 \times \frac{10}{3}\\ &= Rs \: 2800 \end{align*}
\begin{align*}\text{CP of watch = Rs} \: 4000 x \\ &= 4000  2800 \\ &= 1200 \end{align*}
\( \therefore \) CP of calculator = Rs 2800
\(\therefore\) CP of watch = Rs 1200_{Ans.}
Solution:
Marked price (MP) = Rs 1350
Selling Price (SP) = Rs 1282.50
\begin{align*} Discount &= MP SP \\&= 1350  1282.50 \\ &= Rs \: 67.50 \end{align*}
\begin{align*} Discount\% &= \frac{Discount}{MP} \times 100\% \\ &= \frac{67.50}{1350} \times 100 \\ &= 5\% \: \: _{Ans.} \end{align*}
Solution:
Selling price (SP) = Rs 29660
VAT % = 10 %
\begin{align*} \text {Amount of VAT} &= 29660 \times \frac{10}{100} \\ &= Rs \: 2966 \end{align*}
Solution:
Let, MP = Rs x,
VAT = 10%
\begin{align*} x + x \: of \: 10\% &= 17050 \\ or, x + x \times \frac{10}{100} &= 17050 \\ or, \frac{10x + x}{10} &= 17050 \\ or, x &= \frac{17050 \times 10}{11} \\ \therefore x &= Rs \: 15500 \end{align*}
\begin{align*} \text{Amount of VAT } &= Rs 17050  Rs 15500 \\ &= Rs 1550 \: _{Ans.} \end{align*}
Solution:
Let, cost price (CP) = Rs x
VAT = 10%
\begin{align*} x + x \: of \: 10\% &= 650 \\ or, x + x \times \frac{10}{100} &= 650\\ or, \frac{11x}{10} &= 650 \\ or, x &= \frac{650 \times 10}{11}\\ \therefore x &= Rs \: 590.90 \end{align*}
Return money for 1 set = Rs 650  Rs 590.90 = Rs 59.10
Return money for 5 sets = 5 \(\times\) 59.10 = Rs 295.50
Solution:
Price of TV = Rs 24,000
Amount of discount = Rs 1200
Discount % = ?
\begin{align*} Discount\% &= \frac{Discount \: Amount}{Price \: of \: TV} \times 100\% \\ &= \frac{1200}{24000} \times 100\%\\ &= 5\% \end{align*}
\(\therefore \) Discount = 5%
The marked price of a calculator is Rs 260. What is the sale price of it, If 5% discount is allowed?
Solution:
Marked price (MP) = Rs 260
Discount % = 5%
Selling price (SP) = ?
\begin{align*} SP &=MP  MP \: of \: discount\% \\ &= 260  260 \times \frac{5}{100} \\ &= Rs \:260 13 \\&= Rs \: 247 \end{align*}
\(\therefore \) SP = Rs 247 \(_{Ans}\)
Solution:
Let marked price (MP) = Rs x
The price of the article with VAT = Rs 690
VAT =15%
We know that,
The price of the article with \begin{align*} VAT &= x + x \: of \: 15\% \\ 690 &= x + x \times \frac{15}{100} \\ or, 690 &= \frac{23x}{20}\\ or,x &= \frac{690 \times 20}{23} \\ x &= Rs \: 600 \end{align*}
The price excluding VAT is Rs 600.
Solution:
Marked price (MP) = Rs 80,000
Discount = 5%
\begin{align*}Selling\: price \:(SP) &= MP  MP \: of \: discount\% \\ &= Rs 80000  80000 \times \frac{5}{100}\\ &= Rs \: 80,000  4000 \\&= Rs \: 76,ooo \: \: _{Ans.} \: \end{align*}
Solution:
The price of computer before VAT = Rs x, VAT = 15%
Cost of computer after adding VAT = Rs 46000
\begin{align*} x + x \: of \: 15 &= Rs \: 46000\\ or, x + x \times \frac{15}{100} &= Rs \: 46000\\ or, \frac{20x + 3x}{20} &= 46000 \\ or, x &= \frac{46000 \times 20}{23}\\ \therefore x &= Rs \: 40,000 \end{align*}
\(\therefore \) The price of exclusive of the VAT = Rs 40,000 \(_{Ans.}\)
Solution:
Cost price of watch (CP) = Rs 1200
Let, marked price (MP) = Rs x
Discount = 20%
\begin{align*} Selling \: price \: (SP) &= MP  MP \: of \: discount\% \\ or, SP &= Rs \: x  Rs\: x \times \frac{20}{100} \\ SP &= Rs\: \frac{5x x}{5}\\ &= Rs \: \frac{4x}{5} \end{align*}
\begin{align*} Profit &= Rs \: 1200\: of \: \frac{100}{3}\% \\ &= Rs \: 1200\: \times \: \frac{100}{3} \times \frac {1}{100} \\ &= Rs. \: 400 \end{align*}
We know that,
\begin{align*} SP &= CP + Profit \\ or, \frac{4x}{5} &= Rs \: 12000 + Rs. \: 4000 \\ or, x &= Rs \frac{1600 \times 5}{4} \\ &= Rs. 2000 \end{align*}
\(\therefore\) Labbled price of watch = Rs 2000
\(\therefore\) SP = 1200 + 400 = Rs 1600 _{Ans}
Solution:
Cost price of television (CP) = Rs x
\begin{align*}Marked \: price\: (MP) &= x + x\: of \:40\%\\ &= x + x \times \frac{40}{100} \\ &= \frac{5x + 2x}{5}\\ &= \frac{7x}{5} \end{align*}
Discount = 15%
\begin{align*}Selling \: price (SP) &=MP  MP \times Discount\% \\ &= \frac{7x}{5}  \frac{7x}{5} \times \frac{15}{100} \\ &= \frac {7x}{5}  \frac{21x}{100} \\ &= Rs \: \frac{140x  21x}{100} \\ &= Rs \: \frac{119x}{100} \end{align*}
Profit = Rs 950
We know that,
\begin{align*} Profit &= SP  CP\\ or, 950 &= \frac{119x}{100}  x \\ or, 950 &= \frac{119x 100x}{100} \\ or, \frac{19x}{100} &= 950\\ or, x &= \frac{950 \times 100}{19}\\ &= Rs 5000 \end{align*}
The cost price = Rs 5000
Marked price (MP) = \( \frac{7 \times 5000}{5} = Rs \: 7000 \: \: _{Ans}\)
Solution:
Let, marked price (MP) = Rs x
Selling price (SP) = Rs 4250
Discount = 15%
\begin{align*} SP &= MP  MP \: of\: discount\% \\ 4250 &= x x \times \frac{15}{100}\\ or, 4250 &= \frac{20x  3x}{20} \\ or, 4250 &= \frac{17x}{20}\\ or, x &= \frac{4250 \times 20}{17}\\ &= Rs. \: 5000 \end{align*}
Again, Let CP = Rs y
\begin{align*} MP &= CP + CP \: of \: 25\% \\ or, MP &= y + y \times \frac{25}{100} \\ or, MP &= \frac{4y + y}{4} \\ or, MP &= \frac{5y}{4}\\ or, \frac{5y}{4} &= 5000 \\ or, y &= \frac{5000 \times 4}{5}\\ &= 4000 \end{align*}
SP = Rs 4250
CP = Rs 4000
\begin{align*} Profit\% &= \frac{SP  CP}{CP} \times 100\% \\ &= \frac{4250  4000}{4000} \times 100\% \\ &= \frac{250}{40}\% \\ \therefore profit \: percentage &= 6.25\% \end{align*}
Solution:
Let, marked price (MP) = Rs x, discount = 10%
\begin{align*} SP &= MP  MP \: of \: discount\% \\ &= x  x \times \frac{10}{100} \\ &= \frac{10x  x}{10}\\ &= \frac{9x}{10} \end{align*}
\begin{align*} CP_1 &= SP  Profit\\ &= \frac{9x}{10}  8 \end{align*}
Again, MP = SP = Rs x
Profit = Rs 20
\( CP_2 = SP  profit = x  20 \)
Now,
\begin{align*} CP_1 &= CP_2 \\ or, \frac{9x}{10}  8 &= x  20 \\ or, \frac{9x  x}{x} &= 8  20\\ or, \frac{9x  10x}{10} &= 12\\ or, x &= 120 \\ \therefore x &= 120 \\ \text{Putting the value of x in SP } = \frac{9x}{10}\\ SP &= \frac{9 \times 120}{10}\\ &= Rs\: 108\\ \therefore Selling \: price = Rs\: 108_{Ans} \end{align*}
Solution:
For Reshmi
Selling price (SP) = Rs 1350
Loss % = 10%
\begin{align*} CP &= \frac{100 \times SP}{100  L\%} \\ &= \frac{100 \times 1350}{100  10}\\ &= \frac{135000}{90}\\ &=Rs \: 1500 \end{align*}
Reshmi cost price is selling price of Reetu
For Reetu
SP = Rs 1500
Profit % = 20 %
\begin{align*} CP &= \frac{100 \times SP}{100 + P\%} \\ &= \frac{100 \times 1500}{100 + 20}\\ &= \frac{150000}{120}\\ &= Rs \: 1250\end{align*}
\( \therefore \)The cost price = Rs 1250
Solution:
Let, the weight 100 gain while buying the goods. The actual weight of the purchasing goods = 120 gram. Let weights 120 gram while selling the goods but the actual weight of the selling goods = 100 gram.
Let the CP of 1 gram of goods = Rs 1
the CP of 100 gram of goods = Rs 100 x
the CP of 120 gram of goods = Rs 120 x
He sells the goods of costing Rs 100x for Rs 120x
He sells the goods of costing 1 for \( \frac{120x}{100x} \)
He sells the goods of costing 120x for \( \frac{120x}{100x} \times 120x = Rs \: 144x \)
SP of goods = Rs 144x
CP of goods = Rs 100x
\begin{align*} Profit \: \% &= \frac{SP  CP}{CP} \times 100\% \\ &= \frac{144x  100x}{100x} \times 100\% \\ &= 44\% \end{align*}
\(\therefore\) Profit = 44%
Solution:
Let, MP = Rs x, discount = 10%
\begin{align*} SP &= MP  MP \: of \: discount\% \\ &= x x \times \frac{10}{100}\\ &= x  \frac{x}{10}\\ &= \frac{10x  x}{10}\\ &= Rs \frac{9x}{10} \end{align*}
Profit = 5%
\begin{align*} CP &= \frac{SP \times 100}{100 + P%} \\ &= \frac{\frac{9x}{10} \times 100}{100 + 5}\\ &= \frac{90x}{105}\\ &= \frac{6x}{7}\: \: \: \: \: \: \: .........(i) \end{align*}
Again,
\begin{align*} SP &= x  x\: of \: 5\% \\ &= x x \times \frac{5}{100}\\ &= x  \frac{x}{20}\\ &= \frac{20x  x}{20}\\ &= Rs \: \frac{10x}{20} \end{align*}
Profit = Rs 338
\(CP = SP  Profit \: = \frac{19x}{20}  338 \: \: \: \: \: \: \: \: \: \: ......(ii)\)
From eq^{n}(i) and eq^{n} (ii)
\begin{align*} \frac{19x}{20}  338 &= \frac{6x}{7} \\ or, \frac{19x}{20}  \frac{6x}{7} &= 338\\or, \frac{113x  120x}{140} &= 338\\or, 13x &= 388 \times 140\\ or, x &= \frac{47320}{13}\\ x &= Rs \: 3650\end{align*}
Putting value of x in eq^{n} (i)
\begin{align*} CP &= \frac{6x}{7} \\&= \frac{6 \times 3640}{7}\\ \therefore CP &= Rs \: 3120\end{align*}
Solution:
Let, MP = Rs x
Loss = Rs 100
Discount = 10%
\begin{align*} SP &= MP  MP \: of\: discount \\ or, SP &= x  x \times \frac{10}{100} \\ \frac{10x  x}{10}\\ &= Rs \: \frac{9x}{10} \end{align*}
CP_{1} = SP + Loss = \( \frac{9x}{10} + 100 \: \: \: \: .......(i)\)
Again,
discount = 5%
Profit = Rs 100
\begin{align*} SP &= MP  MP \: of \: discount\% \\ &= x x \times \frac{5}{100}\\ &= x  \frac{x}{20}\\ &= \frac{20x  x}{20} \\ \therefore SP &= Rs \: \frac{19x}{20} \\Now, \\ CP_2 &= SP  Profit \\ CP &= \frac{19x}{20}  100 \: \: \: \: \: .......(ii) \end{align*}
From equation (i) and (ii)
\begin{align*}\frac{9x}{10} + 100 &= \frac{19x}{20}  100 \\ or, \frac{19x}{20}  \frac{9x}{10} &= 100 + 100\\ or, \frac{19x  18x}{20}&= 200 \\ or, x &= Rs \: 4000 \end{align*}
Marked price = Rs 4000
\begin{align*} CP &= \frac{9x}{10} + 100 \\ &= \frac{ 9 \times 4000}{10} + 100\\ &= 3600 + 100\\ &= Rs \: 3700_{Ans}\end{align*}
Solution:
Let, CP = Rs x
Loss % = 5%
\begin{align*} SP_1 &= CP  CP \: of \: loss\%\\ &= x  x \times \frac{5}{100} \\ &= \frac{20x  x}{20} \\ &= Rs \: \frac{19x}{20} \end{align*}
If he charge Rs 15 more
\( SP_2 = Rs \: \frac{19x}{20} + 15\)
We know that,
\begin{align*} CP + Profit &= SP_2\\ or, x + x \times \frac{5}{100}&= \frac{19x}{20} + 15 \\ or, \frac{20x + x}{20} &= \frac{19x + 300}{20}\\ or, 21x  19x &= 300\\ or, 2x &= 300\\ or, x &= \frac{300}{2}\\ &= Rs \: 150 \end{align*}
\(\therefore\) The cost price = Rs 150_{Ans.}
Solution:
Let, cost price of 1^{st} radio (CP_{1}) = Rs x
Loss % = 12%
Selling price of 1^{st} radio (SP_{1}) = ?
\begin{align*} SP_1 &= \frac{100  L\%}{100} \times CP_1 \\ &= \frac{100  12}{100} \times x \\ &= \frac{88x}{100}\\ &= Rs \: \frac{22x}{25} \end{align*}
Let cost price of 2^{nd}radio (CP_{2}) = Rs 500  x
Profit % (P%) = 8%
Selling price of 2_{nd}radio (SP_{2}) = ?
\begin{align*} SP_2 &= \frac{100 + P\%}{100} \times CP_2 \\ &= \frac{100 + 8}{100} \times( 500  x) \\ &= \frac{108 \times (500  x)}{100}\\ &= Rs \: \frac{27 (500  x)}{25} \end{align*}
From question,
\begin{align*} \frac{22x}{25} + \frac{27(500  x)}{25} &= 500\\ or, \frac{22x + 13500  27x}{25} &= 500 \\ or, 13500  5x &= 12500 \\ or, 5x &= 13500  12500\\ or, x &= \frac{1000}{5} \\ \therefore x &= Rs \: 200 \end{align*}
Cost price of 1^{st} radio = Rs 200
Cost price of 2^{nd} radio = Rs 500  x = 500  200 = Rs 300_{Ans.}
Solution:
Marked price of a bicycle (MP) = Rs 5550
Discount = 10%
VAT = 15%
After discount,
\begin{align*} Selling \: price \: (SP_1) &= MP  Discount\% \: of \: MP\\ SP_1 &= Rs \: 5550  5550 \times \frac{10}{100} \\ &= 5550  555\\ &= Rs \: 4995 \end{align*}
After, adding VAT
\begin{align*} SP_2 &= SP_1 + VAT\% \:of\: SP_1 \\ &= 4995 + 4995 \times \frac{15}{100}\\ &= Rs \: 4995 + Rs \: 749.30 \\ &= Rs\: 5744.25 \: \: \: \: \: \: _{Ans.} \end{align*}
Solution:
Let, marked price (MP) = Rs x
Discount = 20%
VAT = 10%
After discount,
\begin{align*} Selling \: price \: (SP_1) &= MP  Discount \% \: of \: MP\\ &= Rs \: x  x \times \frac{20}{100} \\ &= x  \frac{x}{5}\\ &= \frac{5x x}{5}\\&= Rs \: \frac{4x}{5} \end{align*}
After adding VAT,
\begin{align*} SP_2 &= SP_1 + VAT\% \: of \: SP_1 \\ or, 2376 &= \frac{4x}{5} + \frac{4x}{5} \times \frac{10}{100}\\ or, 2376 &= \frac{40x + 4x}{50}\\ or, 2376 &= \frac{44x}{50} \\ or, x &= \frac{2376 \times 50}{44} \\ x &= Rs \: 2700 \end{align*}
\(\therefore \) the marked price = Rs 2700 \(_{Ans.}\)
Solution:
Marked price (MP) = Rs 3200
Discount = 8%
After discount,
\begin{align*}Selling \: price \: (SP_1)&= MP  MP\: of \: discount \% \\ &= 3200  256 \\ &= Rs \: 2944 \end{align*}
After adding VAT
\begin{align*}Selling \: price \: (SP_2) &= Sp_1 + SP_1 \: of \: VAT \% \\ &= 2944 + 2940 \times \frac{10}{100}\\ &= Rs \: 2944 + 294.40 \\ &= Rs \: 3238.40 \end{align*}
\(\therefore\) The customer pay for camera = Rs 3238.40 \(_{Ans}\)
Solution:
Let marked price (MP) = Rs x
Discount = 10%
VAT = 15%
After discount,
\begin{align*} Selling \: price\: (SP_2)&= MP  MP \: of \: discount\% \\ &= x  x \times \frac{x}{10}\\ &= \frac{10x  x}{10} \\ &= Rs \: \frac{9x}{10} \end{align*}
After adding VAT
\begin{align*} Selling \: price\: (SP_2) &= SP_1 + SP_1 \: of \: VAT\% \\ 1670 &= \frac{9x}{10} + \frac{9x}{10} \times \frac{15}{100} \\ or, 16750 &= \frac{9x}{10} + \frac{27x}{200}\\ or, 16720 &= \frac{180x + 27x}{200}\\ or, x &= \frac{16720 \times 200}{207} \\ &= Rs \: 16154.50 \end{align*}
\begin{align*} Amount \: of \: discount &= x \: of \: 10\% \\ &= 16154.50 \times \frac{10}{100}\\ &= Rs \: 1615.45 \end{align*}
Solution:
Let, MP = Rs x
Discount = 20%
VAT = 10%
Amount of VAT = Rs 880
After discount,
\begin{align*}Selling\: price \: (SP_1) &= MP  discount\% \:of \: SP_1 \\ &= x  x \times \frac{20}{100}\\ &= x \frac{x}{5}\\ &= \frac{5x x}{5}\\ &= Rs \: \frac{4x}{5}\end{align*}
After adding VAT,
\begin{align*} Selling \: price \: (SP_2)&= SP_1 + VAT\% \:of\: SP_1\\ 880 &= \frac{4x}{5} \times \frac{10}{100}\\ or, 880 &= \frac{4x}{5} + \frac{2x}{25} \\ or, 880&= \frac{20x + 2x}{25}\\ or, 880 &= \frac{22x}{25}\\ or, x &= \frac{880 \times 25}{22}\\ &= Rs \: 1000 \end{align*}
\(\therefore\) Marked price = Rs 1000 \(_{Ans}\)
Solution:
Marked price (MP) = Rs 5000
Discount = 15%
VAT = 10%
\begin{align*} Selling \: price \: (SP_1) &= MP  MP \: of \: discount\% \\ &= 5000  5000 \times \frac{15}{100}\\ &= Rs \: 5000  750\\&= Rs \: 4250\end{align*}
After adding VAT
\begin{align*} Selling \: price \: (SP_2)&= SP_1 + SP_1 \: of\: VAT \\ &= 4250 + 4250 \times \frac {10}{100}\\ &= Rs \: 4250 + Rs \: 425 \\ &= Rs \: 4675 \end{align*}
\(\therefore\) The price of the radio = Rs 4675 \(_{Ans.}\)
Solution:
Let, Marked price = Rs x
\begin{align*}\text{The price after discount} &= xx \times 16\%\\ &= x  x \times \frac{16}{100}\\ &= \frac{25x  4x}{25}\\ &= \frac{21x}{25} \end{align*}
\begin{align*}\text{The price after VAT} &= \frac{21x}{25} + \frac{21x}{25} \times 13\% \\ or, 9492&= \frac{21x}{25 } \frac{21x}{25} \times \frac{13}{100} \\ or, 9492 &= \frac{21x}{25} + \frac{273x}{2500}\\ or, 9492 &= \frac{2100x + 273x}{2500}\\ or, 9492 \times 2500 &= 2373x\\ or, \frac{23730000}{2373} &= x\\ \therefore Market \: price\: (x) &= 1000 \end{align*}
\begin{align*} Amount \: of \: VAT &= \frac{21x}{25} \times \frac{13}{100} \\ &= \frac{21 \times 10000 \times 13}{25 \times 100}\\ &= Rs \: 1092\: \: _{Ans.}\end{align*}
Solution:
Let, marked price (MP) = Rs x
Discount = 15%
VAT = 13%
After discount,
\begin{align*} Selling \: price \: (SP_1) &= MP  discount\%\: of\: MP\\ &= x x \times \frac{15}{100}\\ &= x\frac{3x}{10}\\ &= \frac{20x  3x}{20}\\ &= \frac{17x}{20} \end{align*}
After adding VAT,
\begin{align*} Selling \: price \: (SP_2) &= SP_1 + VAT\% \: of \: (SP_1)\\ 28815 &= \frac{17x}{20} + \frac{17x}{20} \times \frac{13}{100}\\ or, 28815 &= \frac{17x}{20} + \frac{221x}{2000}\\ or, 28815 &= \frac{1921x}{2000}\\ or, x &= \frac{28815 \times 2000}{1921}\\ &= Rs \: 30,000 \end{align*}
\begin{align*} \text{Amount of discount} &= 30,000 \times \frac{15}{100}\\ &= Rs \: 4500 \: \: _{Ans.} \end{align*}
Solution:
Let, Marked price (MP) = Rs x
Discount = 20%
VAT = 10%
After discount
\begin{align*} Selling \: price \: (SP_1) &= MP  Discount\% \: of \: MP\\ &= xx \times \frac{20}{100}\\ &= \frac{5x x}{5} \\ &= Rs \frac{4x}{5} \end{align*}
\begin{align*} Amount\: of \:VAT &= VAT\:of\:SP_1 \\ 440 &= \frac{4x}{5} \times \frac{10}{100}\\ or, 440 &= \frac{2x}{25}\\ or, x &= \frac{440 \times 25}{2}\\ \therefore x &= Rs \: \: 5500 \end{align*}
\(\therefore\) Marked price of the blanket = Rs 5500 \(_{Ans.}\)
Solution:
Let, Marked price (MP) = Rs x
Discount = 20%
VAT = 15%
After discount
\begin{align*} Selling \: price \: (SP_1) &= MP  Discount\% \: of \: MP\\ &= xx \times \frac{20}{100}\\ &= \frac{5x x}{5} \\ &= Rs \frac{4x}{5} \end{align*}
After adding VAT
\begin{align*} Selling \: price\: (SP_2) &= SP_1 + VAT\% \: of \: SP_1 \\ 22080 &= Rs \: \frac{4x}{5} + \frac{4x}{5} \times \frac{15}{100}\\ or, 22080 &= Rs \: \frac{4x}{5} + \frac{12x}{100}\\ or, 22080 &= \frac{80x + 12x}{100}\\ or, 22080 &= \frac{92x}{100}\\ or, x &= \frac{22080 \times 100}{92} \\ x &= Rs \: 24000\end{align*}
Marked price = Rs 24000
\begin{align*} \text{Amount of VAT} &= Rs \: \frac{4x}{5} \times \frac{15}{100}\\ &= \frac{4 \times 24000 \times 5}{5 \times 100}\\ &= Rs \: 2880 \end{align*}
\(\therefore\) Amount of VAT = Rs 2880 \( \: \: _{Ans.}\)
Solution:
The marked price (MP) = Rs 4000
The amount of discount = Rs x
The price of article after discount = Rs (4000  x)
VAT % = 13 %
From question,
\begin{align*} (4000  x) (4000  x) \times \frac{13}{100} &= 3616 \\or, \frac{400000 100x + 52000  13x}{100} &= 3616\\ or, 452000113x &= 361600\\ or, 113x &= 452000  361600\\ or, x &= \frac{90400}{113}\\ \therefore x &= Rs. \: 800\end{align*}
\begin{align*} Percent \: discount &= \frac{Amount \: of \: discount}{MP} \times 100\% \\ &= \frac{800}{4000} \times 100\% \\ &= 20\% \: \: \: _{Ans.} \end{align*}

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25%
15%
20%
10%

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25%
30%
22%
32%

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Rs 2200
Rs2100
Rs2000

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Rs 20
Rs 20

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loss: 37.5%
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Loss:20 %

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Rs 5100
Rs 5500
Rs 5200
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Rs 750
Rs 850
Rs 864
Rs 800

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Rs 2100
Rs 2000
Rs 2400

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P = 4 %
P=7%
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7% loss
9% loss
4% loss
5% loss

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Rs 500, Rs 300
Rs 700,Rs 500
Rs 600, Rs 350
Rs 640, Rs 400

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Rs 350, Rs 400
Rs 275, Rs 375
Rs 200, Rs 300
Rs 100, Rs 150

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Rs 150
Rs 100
Rs 120
Rs 130

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Rs 240
Rs 300
Rs 350
Rs 250

If the selling price of a sofa is increased by Rs 7920; the loss of 15%converts into a profit of 18%.Find the cost price.
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Rs 1850
Rs 1500
Rs 2200

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