Profit And Loss - Arithmetic
Calculation of cost price, sale price, and profit and loss percent
Question (1) An article is sold at the profit of 20%. If the cost price of that article is $500.00, the what is it's sale price?
Solution
Given, Cost price = $ 500.00
And, profit = 20%
Thus, sale price (SP) = ?
We know that,
Sale Price (SP)
Thus, Sale price (SP) of given article
= 120 × 5
= 600
Thus, sale price (SP) = $ 600.00 Answer
Alternate Method (1) to solve the question based on profit and loss
Given, Cost price = $ 500.00
And, profit = 20%
Thus, sale price (SP) = ?
We know that,
Profit = Cost price (CP) × profit %
= 500 × 20%
= 5 × 20 = 100
Thus, profit = $ 100.00
Now, we know that, Sale price (SP) = Cost price (CP) + Profit
Thus, Sale price (SP) of given article = $500 + $100
= $600
Thus, Sale price (SP) = $ 600.00 Answer
Alternate Method (2) to solve the question based on profit and loss
Given, Cost price = $ 500.00
And, profit = 20%
Thus, sale price (SP) = ?
We know that, Sale price (SP) = Cost price + (Cost price × Gain%)
Thus, Sale price (SP) of given article = 500 + (500 × 20%)
= 500 + (5 × 20)
= 500 + 100 = 600
Thus, Sale price (SP) of given article = $600 Answer
Alternate Method (3) to solve the question based on profit and loss
Given, Cost price = $ 500.00
And, profit = 20%
Thus, sale price (SP) = ?
We know that, Sale price (SP) = (100+gain%)% of Cost price (CP)
Thus, Sale price (SP) of given article = (100+20)% of 500
= 120% of 500
= 120 × 5
= 600
Thus, Sale price (SP) of given article = $600.00 Answer
Question (2) An article is sold at the profit of 30%. If the cost price of that article is $800.00, the what is it's sale price?
Solution
Given, Cost price = $ 800.00
And, profit = 30%
Thus, sale price (SP) = ?
We know that,
Sale Price (SP)
Thus, Sale price (SP) of given article
= 130 × 8
= 1040
Thus, sale price (SP) = $1040.00 Answer
Alternate Method (1) to solve the question based on profit and loss
Given, Cost price = $800.00
And, profit = 30%
Thus, sale price (SP) = ?
We know that,
Profit = Cost price (CP) × profit %
= 800 × 30%
= 8 × 30 = 240
Thus, profit = $240.00
Now, we know that, Sale price (SP) = Cost price (CP) + Profit
Thus, Sale price (SP) of given article = $800 + $240
= $1040
Thus, Sale price (SP) = $1040.00 Answer
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 + (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 × 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
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 × 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 × 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)
= 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 × 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)
⇒ 80 m = 120 × 1600
⇒ 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
After cross multiplication, we get
⇒ 7 m = 2100 × 10
⇒ 7 m = 21000
Thus,
⇒ 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 × 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 × 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)
= 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 × 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)
⇒ 70 m = 125 × 2100
⇒ 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)
Thus, cost price of given article
= 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 %
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 × 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
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)
After Cross multiplication, we get
⇒ 85 m = 1020 × 100
⇒ 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
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)
Thus, cost price of given article
= 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 %
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 × 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
=125/25=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)
After Cross multiplication, we get
⇒ 9 m = 2250 × 10
⇒ 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
∴ when cost price is 100, then gain
Thus, gain at 2nd sales price = 5% Answer
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