Profit And Loss

Math-home

Alternate Method (2) to solve the question based on profit and loss

Given, Cost price = $ 800.00

And, profit = 30%

Thus, sale price (SP) = ?

We know that, Sale price (SP) = Cost price + (Cost price × Gain%)

Thus, Sale price (SP) of given article = 800 + (800 × 30%)

`=800 + (\cancel800\ 8xx30/\cancel100)`

= 800 + (8 × 30)

= 800 + 240 = 1040

Thus, Sale price (SP) of given article = $1040 Answer

Alternate Method (3) to solve the question based on profit and loss

Given, Cost price = $800.00

And, profit = 30%

Thus, sale price (SP) = ?

We know that, Sale price (SP) = (100+gain%)% of Cost price (CP)

Thus, Sale price (SP) of given article = (100+30)% of 800

= 130% of 800

`=130/\cancel100xx\cancel800\ 8`

= 130 × 8

= 1040

Thus, Sale price (SP) of given article = $1040.00 Answer

Question (3) If after selling an article for $1600 a person gets a loss of 20%. Thus, to earn a profit of 20% at what price article should be sold?

Solution

Given, Sale price = $1600

And, loss = 20%

Thus, to gain 20% profit, sale price (SP) = ?

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the sale price to earn given profit at the cost price]

Calculation of Cost Price (CP)

Let, cost price of the given article = m

Thus, Cost price – (loss percent of cost price) = Sale price

⇒ m – (20% of m) = 1600

`=> m – 20/100xxm = 1600`

`=>m-m/5=1600`

`=>(5m-m)/5=1600`

`=>(4m)/5=1600`

After cross multiplication, we get

⇒ 4 m = 1600 × 5

⇒ 4 m = 8000

Thus, `m=8000/4`

⇒ m = 2000

Thus, cost price = $2000

Calculation of Sale Price when profit and cost price is known

Now, here, Cost price (CP) = $2000

And, profit = 20%

Thus, Sale price (SP) = ?

Now, net profit = profit % of cost price

= 20% of 2000

`=20/100xx2000`

= 20 × 20 = 400

Thus, profit = $400

Now, we know that, Sale price (SP) = Cost price + Profit

= $2000 + $400

= $2400

Thus, to gain 20% of price the sale price (SP) = $2400 Answer

Method (1) to solve the question based on profit and loss

Given, Sale price = $1600

And, loss = 20%

Thus, to gain 20% profit, sale price (SP) = ?

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the sale price to earn given profit at the cost price]

Calculation of Cost Price (CP)

Let the cost price = $100

Thus, loss 20% = $100 × 20% = $20

Thus, loss = $20

Thus, sale price (SP) = Cost price (CP) – Loss

= $100 – $20 = 80

Thus, sale price (SP) at a loss of 20% = $80

Now,

∵ When, sale price is 80, then cost price = 100

∴ When, sale price is 1, then cost price `=100/80`

∴ When sale price is 1600, then cost price `=100/\cancel80xx\cancel1600\ 20`

= 100 × 20

= 2000

Thus, cost price (CP) = $2000

Calculation of Sale Price when profit and cost price is known

Here, cost price = $2000

And profit = 20%

Now, we know that, Sale Price (SP) `=(text{100 + Gain%})/100xxC.P.`

`=(100+20)/100xx2000`

`=120/100xx2000`

= 120 × 20 = 2400

Thus, Sale price (SP) to earn given profit of 20% = $2400 Answer

Shortcut method (Shortcut Trick) (1) to solve the question based on profit and loss

Given, Sale price = $1600

And, loss = 20%

Thus, to gain 20% profit, sale price (SP) = ?

Let, Cost price = 100

Thus, Loss of 20% at cost price = 100 × 20% = 20

Thus, Sale Price = Cost Price – Loss%

= 100 – 20 = 80

Thus, Sale price at the loss of 20% = 80

Now, Profit of 20% = Cost price × 20%

= 100 × 20% = 20

Thus, Sale Price at profit = Cost price + Profit

= 100 + 20 = 120

Thus, Sale price at 20% profit = 120

Now, When Sale price at 20% loss is 80, then sale price at 20% profit = 120

∴ When, sale price at 20% loss is 1, the sale price at 20% profit `=120/80`

∴ When, sale price at 20% loss is 1600, the sale price at 20% profit `=120/80xx1600`

= 120 × 20 = 2400

Thus, Sale price to gain 20% profit = $2400 Answer

Shortcut method (Shortcut Trick) (2) to solve the question based on profit and loss

Given, Sale price = $1600

And, loss = 20%

Thus, to gain 20% profit, sale price (SP) = ?

Let, Sale Price (SP) = m

Now, we know that, In the case of profit and loss

(100 – Loss%) : (1st SP) = (100 + Gain%) : (2nd SP)

`=> (100-20)/1600 = (100+20)/m`

`=> 80/1600 = 120/m`

⇒ 80 m = 120 × 1600

`=> m = (120xx1600)/80`

⇒ m = 120 × 20

⇒ m = 2400

Thus, Sale Price (SP) at 20% of profit = $2400 Answer

Question (4) A person gets a loss of 30% after selling an article for $2100. Now, to earn a profit of 25% at what price article should be sold?

Solution

Given, Sale price = $2100

And, loss = 30%

Thus, to gain 25% profit, sale price (SP) = ?

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the sale price to earn given profit at the cost price]

Calculation of Cost Price (CP)

Let, cost price of the given article = m

Thus, Cost price – (loss percent of cost price) = Sale price

⇒ m – (30% of m) = 2100

`=> m – 30/100xxm = 2100`

`=>m-(3m)/10=2100`

`=>(10m-3m)/10=2100`

`=>(7m)/10=2100`

After cross multiplication, we get

⇒ 7 m = 2100 × 10

⇒ 7 m = 21000

Thus, `m=21000/7`

⇒ m = 3000

Thus, cost price = $3000

Calculation of Sale Price when profit and cost price is known

Now, here, Cost price (CP) = $3000

And, profit = 25%

Thus, Sale price (SP) = ?

Now, net profit = profit % of cost price

= 25% of 3000

`=25/100xx3000`

= 25 × 30 = 750

Thus, profit = $750

Now, we know that, Sale price (SP) = Cost price + Profit

= $3000 + $750

= $3750

Thus, to gain 25% of price the sale price (SP) = $3750 Answer

Method (1) to solve the question based on profit and loss

Given, Sale price = $2100

And, loss = 30%

Thus, to gain 25% profit, sale price (SP) = ?

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the sale price to earn given profit at the cost price]

Calculation of Cost Price (CP)

Let the cost price = $100

Thus, loss 30% = $100 × 30% = $30

Thus, loss = $30

Thus, sale price (SP) = Cost price (CP) – Loss

= $100 – $30 = 70

Thus, sale price (SP) at a loss of 30% = $70

Now,

∵ When, sale price is 70, then cost price = 100

∴ When, sale price is 1, then cost price `=100/70`

∴ When cost price is 2100, then cost price `=100/\cancel70xx\cancel2100\ 30`

= 100 × 30

= 3000

Thus, Cost Price (CP) = $3000

Calculation of Sale Price when profit and cost price is known

Here, cost price = $3000

And profit = 25%

Now, we know that, Sale Price (SP) `=(text{100 + Gain%})/100xxC.P.`

`=(100+25)/100xx3000`

`=125/100xx3000`

= 125 × 30 = 3750

Thus, Sale price (SP) to earn given profit of 25% = $3750 Answer

Shortcut method (Shortcut Trick) (2) to solve the question based on profit and loss

Given, Sale price = $2100

And, loss = 30%

Thus, to gain 25% profit, sale price (SP) = ?

Let, Cost price = 100

Thus, Loss of 30% at cost price = 100 × 30% = 30

Thus, Sale Price = Cost Price – Loss%

= 100 – 30 = 70

Thus, Sale price at the loss of 30% = 70

Now, Profit of 25% = Cost price × 25%

= 100 × 25% = 25

Thus, Sale Price at profit = Cost price + Profit

= 100 + 25 = 125

Thus, Sale price at 25% profit = 125

Now, When Sale price at 30% loss is 70, then sale price at 25% profit = 125

∴ When, sale price at 30% loss is 1, the sale price at 25% profit `=125/70`

∴ When, sale price at 30% loss is 2100, the sale price at 25% profit `=125/70xx2100`

= 125 × 30 = 3750

Thus, Sale price to gain 25% profit = $3750 Answer

Shortcut method (Shortcut Trick) (2) to solve the question based on profit and loss

Given, Sale price = $2100

And, loss = 30%

Thus, to gain 25% profit, sale price (SP) = ?

Let, Sale Price (SP) = m

Now, we know that, In the case of profit and loss

(100 – Loss%) : (1st SP) = (100 + Gain%) : (2nd SP)

`=> (100-30)/2100 = (100+25)/m`

`=> 70/2100 = 125/m`

⇒ 70 m = 125 × 2100

`=> m = (125xx2100)/70`

⇒ m = 125 × 30

⇒ m = 3750

Thus, Sale Price (SP) at 25% of profit = $3750 Answer

Question (5) After selling an article at $1020, a vendor gets a loss of 15%, if he would sold it for $1140, then find the loss or gain percent.

Solution

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the profit or loss at given sale price.]

Given, 1st Sale price (SP) = $1020

Then Loss = 15%.

And, 2nd Sale price (SP) = $1140

Then, profit% or gain% = ?

Calculation of Cost Price

We know that,

Cost Price (CP) `=100/(text{100 - Loss%})xxSP`

Thus, cost price of given article `=100/(100-15)xx1020`

`=100/85xx1020`

= 100 × 12 = 1200

Thus, Cost Price (CP) = $1200

Calculation of Loss%

Now, As given in the question, 2nd Sales Price (SP) = $1140

This, 2nd Sales price (SP) is less than the cost price, thus vendor gets a loss even after selling at 2nd sales price.

We know that, Loss = Cost price – Sales price

Thus, Loss at the 2nd Sales price (SP) = $1200 – $1140

Thus, Loss on 2nd sales price (SP) = $60

Now, we know that, Loss % `=(text{Loss} xx 100)/(text(C.P.)`

`=(60xx100)/1200=5%`

Thus, Loss % on selling at 2nd sales price = 5% Answer

Method (2) to solve the question based on profit and loss

Given, 1st Sale price (SP) = $1020

Then Loss = 15%.

And, 2nd Sale price (SP) = $1140

Then, profit% or gain% = ?

Calculation of Cost Price

Let, cost price = 100

Thus, 15% loss at the cost price = 15% of 100 = 15

Thus, Sale Price = Cost price – Loss

= 100 – 15

Or, Sale Price at the loss of 15% = 85

Now,

∵ When, sale price at 15% loss is 85, then cost price = 100

∴ When, sale price at 15% loss is 1, then cost price `=100/85`

∴ When sale price at 15% is 1020, then cost price `=100/85xx1020`

= 100 × 12 = 1200

Thus, Cost price = $1200

Calculation of loss %

Since, 2nd sales price ($1140) is less than the cost price

Thus, Loss = Cost Price – Sales price

= $1200 – $1140

Thus, loss at 2nd sales price = $60

∵ when cost price is 1200, the loss = 60

∴ when cost price is 1, then loss `=60/1200`

∴ when cost price is 100, the loss `=60/1200xx100`

`=60/12=5%`

Thus, loss at 2nd sales price = 5% Answer

Method (3) to solve the question based on profit and loss

Given, 1st Sale price (SP) = $1020

Then Loss = 15%.

And, 2nd Sale price (SP) = $1140

Then, profit% or gain% = ?

Calculation of Cost Price

Let, cost price = m

We know that, in the case of Loss,

Sales price = Cost price – (Loss% of Cost price)

⇒ 1020 = m – (15% of m)

`=> 1020 = m-(15/100xxm)`

`=>1020 =m-(15\ m)/100`

`=>1020 = (100\ m-15\ m)/100`

`=>1020 =(85\ m)/100`

After Cross multiplication, we get

⇒ 85 m = 1020 × 100

`=> m = (1020xx100)/85`

⇒ m = 12 × 100 = 1200

Thus, Cost price (CP) = $1200

Calculation of Loss%

Since, 2nd sales price ($1140) is less than the cost price

Thus, Loss = Cost Price – Sales price

= $1200 – $1140

Thus, loss at 2nd sales price = $60

∵ when cost price is 1200, the loss = 60

∴ when cost price is 1, then loss `=60/1200`

∴ when cost price is 100, the loss `=60/1200xx100`

`=60/12=5%`

Thus, loss at 2nd sales price = 5% Answer

Question (6) A shopkeeper gets a loss of 10% when sold a box at $2250. If he would sold the box for $2625, then find the gain or loss percent.

Solution

[Strategy to solve the question: First calculate the cost price at given sale price and loss percent. Then calculate the profit or loss at given sale price.]

Given, 1st Sale price (SP) = $2250

And loss = 10%

Second Sale price (SP) = $2625

Then, loss or gain percent = ?

Calculation of Cost Price

We know that,

Cost Price (CP) `=100/(text{100 - Loss%})xxSP`

Thus, cost price of given article `=100/(100-10)xx2250`

`=100/90xx2250`

= 100 × 25 = 2500

Thus, Cost Price (CP) = $2500

Calculation of Loss%

Now, As given in the question, 2nd Sales Price (SP) = $2625

This, 2nd Sales price (SP) is less than the cost price, thus vendor earns a profit after selling at 2nd sales price.

We know that, Gain = Sale price – Cost price

Thus, Gain at the 2nd Sales price (SP) = $2625 – $2500

Thus, Gain on 2nd sales price (SP) = $125

Now, we know that, Gain % `=(text{Gain} xx 100)/(text(C.P.)`

`=(125xx100)/2500 = 5%`

Thus, Gain % on selling at 2nd sales price = 5% Answer

Method (2) to solve the question based on profit and loss

Given, 1st Sale price (SP) = $2250

And loss = 10%

Second Sale price (SP) = $2625

Then, loss or gain percent = ?

Calculation of Cost Price

Let, cost price = 100

Thus, 10% loss at the cost price = 10% of 100 = 10

Thus, Sale Price = Cost price – Loss

= 100 – 10

Or, Sale Price at the loss of 10% = 90

Now,

∵ When, sale price at 10% loss is 90, then cost price = 100

∴ When, sale price at 10% loss is 1, then cost price `=100/90`

∴ When sale price at 10% is 2250, then cost price `=100/90xx2250`

= 100 × 25 = 2500

Thus, Cost price = $2500

Calculation of Gain %

Since, 2nd sales price ($2625) is more than the cost price

Thus, Gain = Sale price – Cost price

= $2625 – $2500

Thus, gain at 2nd sales price = $125

∵ when cost price is 2500, the gain = 125

∴ when cost price is 1, then gain `=125/2500`

∴ when cost price is 100, the gain `=125/2500xx100`

`=125/25=5%`

Thus, gain at 2nd sales price = 5% Answer

Method (3) to solve the question based on profit and loss

Given, 1st Sale price (SP) = $2250

Then Loss = 10%.

And, 2nd Sale price (SP) = $2625

Then, profit% or gain% = ?

Calculation of Cost Price

Let, cost price = m

We know that, in the case of loss,

Sales price = Cost price – (Loss% of Cost price)

⇒ 2250 = m – (10% of m)

`=> 2250 = m-(10/100xxm)`

`=> 2250 = m-(1/10xxm)`

`=>2250 =m-1/10 m`

`=>2250 = (10\ m-m)/10`

`=>2250 =(9\ m)/10`

After Cross multiplication, we get

⇒ 9 m = 2250 × 10

`=> m = (2250xx10)/9`

⇒ m = 250 × 10 = 2500

Thus, Cost price (CP) = $2500

Calculation of Gain%

Since, 2nd sales price ($2625) is mre than the cost price

Thus, Gain = Sales Price – Cost price

= $2625 – $2500

Thus, gain at 2nd sales price = $125

∵ when cost price is 2500, the gain = 125

∴ when cost price is 1, then gain `=125/2500`

∴ when cost price is 100, then gain `=125/2500xx100`

`=125/25=5%`

Thus, gain at 2nd sales price = 5% Answer

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Math-home

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