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
\(S.P = \frac {C.P \times (100 + P\%)} {100}\: {or}\: S.P = \frac {C.P \times (100 - L\%)} {100}\)
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.
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 \(_{Ans.}\)
An article is bought for Rs 800 & sold for 5/4 of the cost price. What is the profit percentage?
10%
25%
15%
20%
If a dozen is bought for Rs. 48 and sold for Rs 5 per piece, what percent is the profit?
22%
32%
30%
25%
Raman sold a camera for Rs. 2520 at 5% profit. Find the cost price.
Rs2000
Rs 2200
Rs 2400
Rs2100
Shila brought 5 books for Rs 1500 and sold them at 20% loss, Find the selling price of the book.
Rs 15
Rs 20
Rs 25
Rs 20
If the cost price of 10 chairs is equal to the selling price of 16 chairs, find the loss or gain percentage.
Loss:25 %
Loss:30%
Loss:20 %
loss: 37.5%
By selling a watch for Rs 4500 a dealer got 10% loss. At what price should he sell it so as to gain 10%?
Rs 5500
Rs 5100
Rs 5200
Rs 4500
Sohan bought a radio for Rs. 800 and sold it to Rohan at profit of 20% Rohan sold it to Mohan at a loss of 10%. For how much did Mohan buy it?
Rs 800
Rs 864
Rs 850
Rs 750
Amisha sold a cycle to Amir at a profit of 10%. Amir sold the same cycle to Abhishek at a profit of 20%. If Abhishek has sold it for Rs 3300 thereby earning a profit of 25% find the cost price of Amisha .
Rs 1550
Rs 2000
Rs 2100
Rs 2400
Salman sold two computer for RS 2400 each. On one he gained 20% and on the other he lost 20% and on the other he lost 20%. Find his gain or loss percentage in the whole transaction.
P=7%
P = 4 %
P=5%
P= 3%
Lata bought two watches for Rs. 800.She sold them to gain 20% on one and lose 20% the other. Calculate her final gain or loss percent if the selling price of both the watches is the same.
7% loss
9% loss
5% 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 640, Rs 400
Rs 500, Rs 300
Rs 700,Rs 500
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 275, Rs 375
Rs 100, Rs 150
Rs 350, Rs 400
Rs 200, Rs 300
A man bought a hen and a duck for Rs. 370 and sold them for Rs.402, thereby gaining 20% on the former and losing 15% on the later. Find the cost price of the duck.
Rs 120
Rs 130
Rs 150
Rs 100
A person sold an article at a profit of 15% .If he sold it for Rs 81 less, his loss would have been 12% Find the cost price of the article.
Rs 240
Rs 350
Rs 250
Rs 300
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.
Rs 24000
Rs 1500
Rs 2200
Rs 1850
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Sachin shah
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