Videos Related with Profit and loss

Note on Profit and loss

  • Note
  • Things to remember
  • Videos
  • Exercise
  • Quiz

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.

  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%
  • An article is bought for Rs 800 & sold for 5/4 of the cost price. What is the profit percentage?

    20%


    15%


    10%


    25%


  • If a dozen is bought for Rs. 48 and sold for Rs 5 per piece, what percent is the profit?

    25%


    22%


    32%


    30%


  •  Raman sold a camera for Rs. 2520 at 5% profit. Find the cost price.

    Rs 2400


    Rs2000


    Rs 2200


    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: 37.5%


     Loss:20 % 


    Loss:30%


  • 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 5100


    Rs 4500


    Rs 5200


    Rs 5500


  • 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 864


    Rs 800


    Rs 750


    Rs 850


  • 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 2400


    Rs 2000


    Rs 2100


  • 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= 3%


    P=5%


  • 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.

    4% loss 


    9% loss 


    7% loss 


    5% 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 500, Rs 300


    Rs 600, Rs 350


    Rs 640, Rs 400


    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 130


    Rs 150


    Rs 100


    Rs 120


  • 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 300


    Rs 250


    Rs 350


  • 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 1850


    Rs 2200


  • You scored /15


    Take test again

DISCUSSIONS ABOUT THIS NOTE

You must login to reply

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


You must login to reply

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.


You must login to reply

By selling 75 apples a seller gains the selling price of 15 apples. Find his grain percentage

Solve questionBy selling 75 apples a seller gains the selling price of 15 apples. Find his gain percentage


You must login to reply

A money lender borrows a certain sum of money at 3% per annum simple interest and invests the same sum at 5% per anuum compound interest. If he makes a profit of Rs 1082 after 3 yes.


You must login to reply