## Note on Profit and loss

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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 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.

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.
.

### Very Short Questions

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:

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 (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:

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 $$_{Ans.}$$

0%

10%

20%

15%

25%

32%

30%

25%

22%

Rs2000

Rs 2400

Rs 2200

Rs2100

Rs 15

Rs 20

Rs 25

Rs 20

Loss:30%

loss: 37.5%

Loss:25 %

Loss:20 %

Rs 5500

Rs 5100

Rs 5200

Rs 4500

Rs 850

Rs 864

Rs 750

Rs 800

Rs 2000

Rs 2400

Rs 1550

Rs 2100

P=7%

P=5%

P = 4 %

P= 3%

5% loss

7% loss

9% loss

4% loss

• ### A man bought two books for Rs 1040. He sold one at a loss of 15% and the other at a profit of 36% then he found that each book was  sold for the same price. Find the cost  price of each book.

Rs 600, Rs 350

Rs 500, Rs 300

Rs 700,Rs 500

Rs 640, Rs 400

• ### Rambilash bought two radio sets for Rs  500. He sold one at a loss  of 12% and the  other at a gain of 8%. He neither gained nor lost on his transaction.Find the cost price  of each radio.

Rs 200, Rs 300

Rs 100, Rs 150

Rs 350, Rs 400

Rs 275, Rs 375

Rs 120

Rs 150

Rs 130

Rs 100

Rs 240

Rs 300

Rs 250

Rs 350

Rs 2200

Rs 24000

Rs 1850

Rs 1500

• ## You scored /15

Forum Time Replies Report
##### Sachin shah

A mobile phine set after allowing 10% discount on its marked price was sold a gain of 30% had it been sold after allowing 20% discount there would have been a profit of rs 350.find the cost price of mobile set

##### Nabraj baral

After allowing 20% discount on the marked price of watch, the value of the watch will be 're.2376 , when a vat 10% is added. Find its marked price.