Mathematics

Profit And Loss

Math-home

How to calculate cost price

Question (1) A watch is sold at $55 with a profit of 10%. Find its cost price?

Solution:

Given, Sale price (SP) = $55

Profit = 10%

Cost price (CP) = ?

We know that,

math profit and loss cost price

Thus, CP `=100/(100+10)xx55`

`=(100xx55)/110`

`=100/2 = 50`

Thus, Cost Price = $50 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $55

Profit = 10%

Cost price (CP) = ?

Let, Cost price = $100

Thus, profit = 10% = $10

Thus, Sale Price = Cost Price + Profit

= 100 + 10 = $110

Now,

∵ When sale price is $110, then cost price = $100

∴ When sale price is $1, then cost price `=100/110=10/11`

∴ When sale price is $55, then cost price `=10/11xx55`

= 10 × 5 = 50

Thus, Cost Price (CP) = $50 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $55

Profit = 10%

Cost price (CP) = ?

Let cost price = x

Therefore, cost price + (10% of cost price) = sale price

⇒ x + 10% of x = $55

`=>x+10/100xx\x= 55`

`=>(100x+10x)/100=55`

`=>(110x)/100=55`

After cross multiplication, we get

110 `x` = 55 × 100

`=>x = (55xx100)/110=100/2`

Thus, `x` = 50

Thus, cost price = $50 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $55

Profit = 10%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a gain of say, 10%, then Sale Price (SP) = 110% of Cost Price (CP)

Here, since profit is equal to 10%

Thus, SP = 110% of CP

⇒ 55 = 110% of C

`=>55 = 110/100xxC`

After cross multiplication, we get

55 × 100 = 110 × C

⇒ 110 × C = 55 × 100

`=> C = (55xx100)/110`

`=>C = 100/2=50`

Thus, Cost Price = $50 Answer

Question (2) A computer is sold at $625. If in this deal the seller earns a profit of 25%, then what is the cost price of that computer?

Solution:

Given, Sale price (SP) = $625

Profit = 25%

Cost price (CP) = ?

We know that,

math profit and loss cost price a

Thus, CP `=100/(100+25)xx625`

`=(100xx625)/125`

= 100 × 5 = 500

Thus, Cost Price = $500 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $625

Profit = 25%

Cost price (CP) = ?

Let, Cost price = $100

Thus, profit = 25% = $25

Thus, Sale Price = Cost Price + Profit

= 100 + 25 = $125

Now,

∵ When sale price is $125, then cost price = $100

∴ When sale price is $1, then cost price `=100/125`

∴ When sale price is $625, then cost price `=100/125xx625`

= 100 × 5 = 500

Thus, Cost Price (CP) = $500 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $625

Profit = 25%

Cost price (CP) = ?

Let cost price = x

Therefore, cost price + (25% of cost price) = sale price

⇒ x + 25% of x = $625

`=>x+25/100xx\x= 625`

`=>(100\ x+25\ x)/100=625`

`=>(125x)/100=625`

After cross multiplication, we get

125 `x` = 625 × 100

`=>x = (625xx100)/125`

⇒ `x` = 5 × 100

Thus, `x` = 500

Thus, cost price = $500 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $625

Profit = 25%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a gain of say, 10%, then Sale Price (SP) = 110% of Cost Price (CP)

Here, since profit is equal to 25%

Thus, SP = 125% of CP

⇒ 625 = 125% of C

`=>625 = 125/100xxC`

After cross multiplication, we get

625 × 100 = 125 × C

⇒ 125 × C = 625 × 100

`=> C = (625xx100)/125`

`=>C = 5xx100` = 500

Thus, Cost Price = $500 Answer

Question (3) If after selling a computer for $1380 a person gets a profit of 15%, then what is the cost price of the computer?

Solution

Given, Sale price (SP) = $1380

Profit = 15%

Cost price (CP) = ?

We know that,

math profit and loss cost price b

Thus, CP `=100/(100+15)xx1380`

`=(100xx1380)/115`

`=(20xx1380)/23`

= 20 × 60 = 1200

Thus, Cost Price = $1200 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1380

Profit = 15%

Cost price (CP) = ?

Let, Cost price = $100

Thus, profit = 15% = $15

Thus, Sale Price = Cost Price + Profit

= 100 + 15 = $115

Now,

∵ When sale price is $115, then cost price = $100

∴ When sale price is $1, then cost price `=100/115`

∴ When sale price is $1380, then cost price `=100/115xx1380`

`=(20xx1380)/23`

= 20 × 60 = 1200

Thus, Cost Price = $1200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1380

Profit = 15%

Cost price (CP) = ?

Let cost price = `x`

Therefore, cost price + (15% of cost price) = sale price

⇒ `x` + 15% of `x` = $1380

`=>x+15/100xx\x= 1380`

`=>(100\ x+15\ x)/100=1380`

`=>(115x)/100=1380`

After cross multiplication, we get

115 `x` = 1380 × 100

`=>x = (1380xx100)/115`

`=>x=(1380xx20)/23`

⇒ `x` = 60 × 20

Thus, `x` = 1200

Thus, cost price = $1200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1380

Profit = 15%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a gain of say, 10%, then Sale Price (SP) = 110% of Cost Price (CP)

Here, since profit is equal to 15%

Thus, SP = 115% of CP

⇒ 1380 = 115% of C

`=>1380 = 115/100xxC`

After cross multiplication, we get

1380 × 100 = 115 × C

⇒ 115 × C = 1380 × 100

`=> C = (1380xx100)/115`

`=>C = (1380xx20)/23`

⇒ C = 60 × 20 = 1200

Thus, Cost Price = $1200 Answer

Question (4) If after selling a bicycle at $1080, seller gets a loss of 10%. Then find the cost price of the bicycle.

Solution

Given, Sale price (SP) = $1080

Loss = 10%

Cost price (CP) = ?

We know that,

math profit and loss cost price c

Thus, CP `=100/(100-10)xx1080`

`=(100xx1080)/ 90`

= 100 × 12 = 1200

Thus, Cost Price = $1200 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) and Sale Price (SP)

Given, Sale price (SP) = $1080

Loss = 10%

Cost price (CP) = ?

Let, Cost price = $100

Thus, Loss = 10% = $10

Thus, Sale Price = Cost Price – Loss

= 100 – 10 = $90

Now,

∵ When sale price is $90, then cost price = $100

∴ When sale price is $1, then cost price `=100/90`

∴ When sale price is $1080, then cost price `=100/90xx1080`

= 100 × 12 = 1200

Thus, Cost Price = $1200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1080

Loss = 10%

Cost price (CP) = ?

Let cost price = `x`

Therefore, cost price – (10% of cost price) = sale price

⇒ `x` – 10% of `x` = $1080

`=>x-10/100xx\x= 1080`

`=>(100\ x-10\ x)/100=1080`

`=>(90x)/100=1080`

After cross multiplication, we get

90 `x` = 1080 × 100

`=>x = (1080xx100)/90`

⇒ `x` = 12 × 100

Thus, `x` = 1200

Thus, cost price = $1200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1080

Loss = 10%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a loss of say, 10%, then Sale Price (SP) = 90% of Cost Price (CP)

Here, since profit is equal to 10%

Thus, SP = 90% of CP

⇒ 1080 = 90% of C

`=>1080 = 90/100xxC`

After cross multiplication, we get

1080 × 100 = 90 × C

⇒ 90 × C = 1080 × 100

`=> C = (1080xx100)/90`

⇒ C = 12 × 100 = 1200

Thus, Cost Price = $1200 Answer

Question (5) A shopkeeper sold an article for $1275. If in this deal shopkeeper has a loss of 15%, then what is the cost price of that article?

Solution

Given, Sale price (SP) = $1275

Loss = 15%

Cost price (CP) = ?

We know that,

math profit and loss cost price d

Thus, CP `=100/(100-15)xx1275`

`=(100xx1275)/ 85`

`=(100xx17xx5xx15)/(17xx5)`

= 100 × 15 = 1500

Thus, Cost Price = $1500 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) and Sale Price (SP)

Given, Sale price (SP) = $1275

Loss = 15%

Cost price (CP) = ?

Let, Cost price = $100

Thus, Loss = 15% = $15

Thus, Sale Price = Cost Price – Loss

= 100 – 15 = $85

Now,

∵ When sale price is $85, then cost price = $100

∴ When sale price is $1, then cost price `=100/85`

∴ When sale price is $1275, then cost price `=100/85xx1275`

`=(100xx17xx5xx15)/(17xx5)`

= 100 × 15 = 1500

Thus, Cost Price = $1500 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1275

Loss = 15%

Cost price (CP) = ?

Let cost price = `x`

Therefore, cost price – (15% of cost price) = sale price

⇒ `x` – 15% of `x` = $1275

`=>x-15/100xx\x= 1275`

`=>(100\ x-15\ x)/100=1275`

`=>(85x)/100=1275`

After cross multiplication, we get

85 `x` = 1275 × 100

`=>x = (1275xx100)/85`

⇒ `x` = 15 × 100

Thus, `x` = 1500

Thus, cost price = $1500 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $1275

Loss = 15%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a loss of say, 10%, then Sale Price (SP) = 90% of Cost Price (CP)

Here, since profit is equal to 15%

Thus, SP = 85% of CP

⇒ 1275 = 85% of C

`=>1275 = 85/100xxC`

After cross multiplication, we get

85 × C = 1275 × 100

`=> C = (1275xx100)/85`

`=> C = (17xx5xx15xx100)/(17xx5)`

C = 100 × 15 = 1500

Thus, Cost Price = $1500 Answer

Question (6) If at a loss of 20% a shopkeeper sold an article for $160, then find the cost price of that article.

Solution

Given, Sale price (SP) = $160

Loss = 20%

Cost price (CP) = ?

We know that,

math profit and loss cost price e

Thus, CP `=100/(100-20)xx160`

`=(100xx160)/80`

= 100 × 2 = 200

Thus, Cost Price = $200 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) and Sale Price (SP)

Given, Sale price (SP) = $160

Loss = 20%

Cost price (CP) = ?

Let, Cost price = $100

Thus, Loss = 20% = $20

Thus, Sale Price = Cost Price – Loss

= 100 – 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 $160, then cost price `=100/80xx160`

= 100 × 2 = 200

Thus, Cost Price = $200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $160

Loss = 20%

Cost price (CP) = ?

Let cost price = `x`

Therefore, cost price – (20% of cost price) = sale price

⇒ `x` – 20% of `x` = $160

`=>x-20/100xx\x= 160`

`=>(100\ x-20\ x)/100=160`

`=>(80x)/100=160`

After cross multiplication, we get

80 `x` = 160 × 100

`=>x = (160xx100)/80`

⇒ `x` = 2 × 100

Thus, `x` = 200

Thus, cost price = $200 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $160

Loss = 20%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a loss of say, 10%, then Sale Price (SP) = 90% of Cost Price (CP)

Here, since profit is equal to 20%

Thus, SP = 80% of CP

⇒ 160 = 80% of C

`=>160 = 80/100xxC`

After cross multiplication, we get

80 × C = 160 × 100

`=> C = (160xx100)/80`

C = 2 × 100 = 200

Thus, Cost Price = $200 Answer

Question (7) Find the cost price of cheese if it is sold for $18 per kg after a loss of 10%.

Solution

Given, Sale price (SP) = $18

Loss = 10%

Cost price (CP) = ?

We know that,

math profit and loss cost price f

Thus, CP `=100/(100-10)xx18`

`=(100xx18)/90`

= 10 × 2 = 20

Thus, Cost Price = $20 Answer

Alternate Method (Unitary Method) to Calculate Cost Price(CP) and Sale Price (SP)

Given, Sale price (SP) = $18

Loss = 10%

Cost price (CP) = ?

Let, Cost price = $100

Thus, Loss = 10% = $10

Thus, Sale Price = Cost Price – Loss

= 100 – 10 = $90

Now,

∵ When sale price is $90, then cost price = $100

∴ When sale price is $1, then cost price `=100/90`

∴ When sale price is $18, then cost price `=100/90xx18`

= 10 × 2 = 20

Thus, Cost Price = $20 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $18

Loss = 10%

Cost price (CP) = ?

Let cost price = `x`

Therefore, cost price – (10% of cost price) = sale price

⇒ `x` – 10% of `x` = $18

`=>x-10/100xx\x= 18`

`=>(100\ x-10\ x)/100=18`

`=>(90x)/100=18`

After cross multiplication, we get

90 `x` = 18 × 100

`=>x = (18xx100)/90`

⇒ `x` = 2 × 10

Thus, `x` = 20

Thus, cost price = $20 Answer

Alternate Method to Calculate Cost Price(CP) or Sale Price (SP)

Given, Sale price (SP) = $18

Loss = 10%

Cost price (CP) = ?

Let Cost Price = C

We know that, If an article is sold at a loss of say, 10%, then Sale Price (SP) = 90% of Cost Price (CP)

Here, since profit is equal to 10%

Thus, SP = 90% of CP

⇒ 18 = 90% of C

`=>18 = 90/100xxC`

After cross multiplication, we get

90 × C = 18 × 100

`=> C = (18xx100)/90`

C = 2 × 10 = 20

Thus, Cost Price = $20 Answer

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