Notes on Profit and Loss | Grade 9 > Compulsory Maths > Arithmetic | KULLABS.COM

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Introduction

In our locality, we can find varieties professions. Every people involved in business wants to profit from their business. But is not sure that every business has profit some may go on the loss. Generally, business is the matter of profit and loss. In business, every people's motive is earning a profit. Here, cost price (C.P.) is the invested amount in business. Then Selling Price (S.P.) must be more than cost price to make a profit.

Profit

When the selling price is greater than the cost price i.e. S.P. > C.P. then, there is profit.

$$\therefore$$ Profit = S.P. - C.P.

and Profit Percentage= $$\frac{Profit\; amount}{cost\;price\;(C.P.)}$$ × 100%

Loss

When the selling price is less than the cost price i.e. S.P. < C.P. then, there is a loss.

$$\therefore$$ Loss = C.P. - S.P.

and Loss Percentage = $$\frac{Loss\;amount}{cost\;price\;(C.P.)}$$ × 100%

Some of the conclusion:

i) When S.P. > C.P., then

1. Profit = S.P. - C.P.
2. C.P. = S.P. - Profit
3. S.P. = C.P. + .Profit

ii) When S.P. < C.P., then

1. Loss = C.P. - S.P.
2. S.P. = C.P. - Loss
3. C.P. = S.P. + Loss

iii) Profit Percentage = $$\frac{Profit\;amount}{cost\;price\;(C.P.)}$$ × 100% = $$\frac{S.P. - C.P.}{C.P.}$$ × 100%

iv) Loss Percentage = $$\frac{Loss\;amount}{cost\;price\;(C.P.)}$$ × 100% = $$\frac{C.P. - S.P.}{C.P.}$$ × 100%

Calculation of SP and CP when profit or loss percentage are given:

i) When CP and Profit percent is given, then SP = $$\frac{100 + P%}{100}$$ × CP

ii) When CP and Loss percent is given, then SP = $$\frac{100 - L%}{100}$$ × CP

iii) When SP and Profit percent is given, then CP = $$\frac{SP × 100}{100 + P%}$$

iv) When SP and Loss percent is given, then CP = $$\frac{SP × 100}{100 - L%}$$

We can solve the profit and loss related sums using percentage as well as unitary method.

• When the selling price is greater than the cost price i.e. S.P. > C.P. then, there is profit.
• When the selling price is less than the cost price i.e. S.P. < C.P. then, there is a loss.
• Profit = S.P. - C.P.
• Profit Percentage= $$\frac{Profit \;amount}{cost\; price(C.P.)}$$ × 100%
• Loss = C.P. - S.P.
• Loss Percentage = $$\frac{Loss\; amount}{cost \;price(C.P.)}$$ × 100%
.

Click on the questions below to reveal the answers

Solution:

Cost Price (CP) = Rs. 1,000

Selling Price (SP) = Rs. 1,200

Here SP > CP

∴ Profit = SP - CP

= Rs. 1,200 - Rs. 1,000

= Rs. 200

Now,

Profit percentage = ($$\frac{Profit}{C.P.}$$ * 100)%

= ($$\frac{200}{1000}$$ * 100)%

= 20%

∴ Profit percentage = 20%

Solution:

Cost Price (CP) = Rs. 2,000

Selling Price (SP) = Rs. 1,500

Here CP > SP

∴ Loss = CP - SP

= Rs. 2,000 - Rs. 1,500

= Rs. 500

Now,

Loss percentage = ($$\frac{Loss{C.P.}$$ * 100)%

= ($$\frac{500}{2000}$$ * 100)%

= 20%

∴ Loss percentage = 25%

Solution:

Cost Price (CP) = Rs. 1,000

Selling Price (SP) = Rs. 1,500

Here SP > CP

∴ Profit = SP - CP

= Rs. 1,500 - Rs. 1,000

= Rs. 500

Now,

Profit percentage = ($$\frac{Profit}{C.P.}$$ * 100)%

= ($$\frac{500}{1000}$$ * 100)%

= 50%

∴ Profit percentage = 50%

Solution:

Cost Price (CP) = Rs. 1,000

Selling Price (SP) = Rs. 800

Here CP > SP

∴ Loss = SP - CP

= Rs. 1,000 - Rs. 800

= Rs. 200

Now,

Loss percentage = ($$\frac{Loss}{C.P.}$$ * 100)%

= ($$\frac{200}{1000}$$ * 100)%

= 20%

∴ Profit percentage = 20%

Solution:

Cost Price (CP) = Rs 400

Selling Price (SP) = Rs 500

∴ SP > CP so, Ram made a profit

∴ Profit = SP - CP

= Rs 500 - Rs 400

= Rs 100

Again, Profit percentage = ($$\frac{Profit}{C.P.}$$ * 100)%

= ($$\frac{100}{400}$$ * 100)%

= 25%

Hence, Ram made a profit percentage of 25%.

Solution:

Cost price of radio (CP) = Rs 5000

Profit percentage (P%) = 10

Selling price of radio (SP) = ?

Now,

SP = $$\frac{100 + P%}{100}$$ * CP

= $$\frac{100 + 10}{100}$$ * 5000

= $$\frac{110}{100}$$ *5000

= Rs 5500

Hence, The selling price of radio is Rs 5500.

Solution:

Cost price of TV (CP) = Rs 25000

Profit percentage (P%) =8

Selling price of TV (SP) = ?

Now,

SP = $$\frac{100 + P%}{100}$$ * CP

= $$\frac{100 + 8}{100}$$ * 25000

= $$\frac{108}{100}$$ * 25000

= Rs 27000

Hence, The selling price of TV to Santoshi is Cost price to Shiya. Therefore cost price for Shiya is Rs 27000.

Solution:

Cost Price of Washing Machine (CP) = Rs 50000

Selling Price ofWashing Machine (SP) = Rs 35000

Since, CP > SP there is loss

Loss = CP - SP

= 50000 - 35000

= 15000

Again,

Loss Percentage =($$\frac{Loss }{C.P.}$$ * 100)%

=($$\frac{15000}{50000}$$ * 100)%

= 30%

Hence, She sold it to Maya at 30% loss.

Solution:

Selling price (SP) = Rs 5,000

Loss = Rs 1,000

Cost price (CP) = ?

Now,

CP = SP +Loss

= Rs 5,000 +Rs 1000

= Rs 6,000

Solution:

1 dozen copies = 12 piece of copies

20 dozen copies = 12 * 20 = 240 piece of copies

Then,

1 dozen = 12 copies = Rs 240

1 copy = $$\frac {240}{12}$$ = Rs 20

240 copy = Rs 20 * 240 = Rs 4800

Total Cost price (CP) = Rs 4800

Now,

Selling price of 1 copy = Rs 30

Selling price of 240 cpoies = Rs 30 * 240 = Rs 7200

Total Selling price (SP) = Rs 7200

∴ SP > CP

Here,

Profit = SP - CP

= Rs 7200 - Rs 4800

= Rs 2400

Hence, She made profit of Rs 2400 on the transaction.

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Benefits

after selling a television on its marked price a shopkeeper makes a profit of 25% but on allowing 10%discount he makes a profit Rs. 230. Find the cost price of the television?