Profit and loss

Subject: Compulsory Mathematics

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Overview

Profit may refer to the difference between purchase price and cost price of bringing to market. Loss can be define as the act of losing.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 labelled price. Value Added Tax is a tax imposed by the government based on goods and services in each step of production and distribution.

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.

\(\text {Loss percentage} = \frac {Loss} {C.P}\times 100\)

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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

\(S.P = \frac {C.P \times (100 + P\%)} {100}\: {or}\: S.P = \frac {C.P \times (100 - L\%)} {100}\)

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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 ]

\(\text {Discount percentage} = \frac {Discount} {M.P} ×100%\)

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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.

Things to remember
  1. Profit or Gain = Selling Price - Cost Price
           P = S.P - C.P
  2. Profit  percentage = \(\frac {Profit}{C.P} \times 100 \)
  3. Loss = Cost price - Selling Price
           L = C.P - S.P
  4. Loss percentage = \(\frac {Loss}{C.P} \times 100 \)
  5. Cost of goods or selling price = original cost + VAT
  6. Rate of VAT = \(\frac{VAT\; amount}{cost\; after\; discount\; (S.P)}\) \(\times\) 100%
  7. Vat Amount = Rate of VAT \(\times\) Discount price.
  8. The cost price of an article is constant.
  9. VAT is levied on discounted price.
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Questions and Answers

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 560Ans.

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*}

\(\therefore SP\) = 5850Ans.

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 = 3325Ans

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:

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:

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, 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 eqn(i) and eqn (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 eqn (i)

\begin{align*} CP &= \frac{6x}{7} \\&= \frac{6 \times 3640}{7}\\ \therefore CP &= Rs \: 3120\end{align*}

Solution:

Let, cost price of calculator (CP1) = Rs x

Cost price of the watch (CP2) = 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 1200Ans.

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*}

CP1 = 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 150Ans.

Solution:

Let, cost price of 1st radio (CP1) = Rs x
Loss % = 12%
Selling price of 1st radio (SP1) = ?

\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 2ndradio (CP2) = Rs 500 - x
Profit % (P%) = 8%
Selling price of 2ndradio (SP2) = ?

\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 1st radio = Rs 200
Cost price of 2nd radio = Rs 500 - x = 500 - 200 = Rs 300Ans.

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%

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:

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} &= x-x \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\\ &= x-x \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\\ &= x-x \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, 452000-113x &= 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*}

Quiz

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