Profit And Loss - Arithmetic

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,

Thus, CP

=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 × 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

After cross multiplication, we get

110 x = 55 × 100

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

After cross multiplication, we get

55 × 100 = 110 × C

⇒ 110 × C = 55 × 100

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,

Thus, CP

= 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 × 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

After cross multiplication, we get

125 x = 625 × 100

⇒ 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

After cross multiplication, we get

625 × 100 = 125 × C

⇒ 125 × C = 625 × 100

= 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,

Thus, CP

= 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

= 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

After cross multiplication, we get

115 x = 1380 × 100

⇒ 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

After cross multiplication, we get

1380 × 100 = 115 × C

⇒ 115 × C = 1380 × 100

⇒ 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,

Thus, CP

= 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 × 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

After cross multiplication, we get

90 x = 1080 × 100

⇒ 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

After cross multiplication, we get

1080 × 100 = 90 × C

⇒ 90 × C = 1080 × 100

⇒ 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,

Thus, CP

= 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 × 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

After cross multiplication, we get

85 x = 1275 × 100

⇒ 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

After cross multiplication, we get

85 × C = 1275 × 100

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,

Thus, CP

= 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 × 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

After cross multiplication, we get

80 x = 160 × 100

⇒ 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

After cross multiplication, we get

80 × C = 160 × 100

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,

Thus, CP

= 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

= 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

After cross multiplication, we get

90 x = 18 × 100

⇒ 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

After cross multiplication, we get

90 × C = 18 × 100

C = 2 × 10 = 20

Thus, Cost Price = $20 Answer