Profit And Loss
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,
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,
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,
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,
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,
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,
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,
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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