Profit And Loss - Arithmetic

Question (1) A person purchases a dinner set at $5, to get 60% profit in how much cost he must sell that dinner set?

Solution

Given, cost price of dinner set = $5

Therefore the sale price to get 60% profit = ?

Thus, the sale price to earn 60% profit = 160% of cost price

= 160% of $5

= 1.6 × 5 = $8

Thus, sale price to get 60% profit = $8 Answer

Alternate method to solve the question of profit and loss

Given, cost price of dinner set = $5

Therefore the sale price to get 60% profit = ?

Now, profit = 60% of cost price

= 60% of $5

= 0.6 × $5

⇒ Profit = $3

Thus, Sale price = cost price + profit

= $5 + $3 = $8

Thus, sale price to get 60% profit = $8 Answer

Question (2) A person bought a cycle for $120. If he wants to get 40% profit on it then in how many dollars will he have to sell it?

Solution

Given, cost price of dinner set = $120

Therefore the sale price to get 40% profit = ?

Thus, the sale price to get 40% profit = 140% of cost price

= 140% of $120

= 14 × 12

= $168

Thus, sale price to get 40% profit = $168 Answer

Alternate method to solve the question of profit and loss

Given, cost price of dinner set = $120

Therefore the sale price to get 40% profit = ?

Now, profit = 40% of cost price

= 40% of $120

= 4 × $12

⇒ Profit = $48

Thus, Sale price = cost price + profit

= $120 + $48 = $168

Thus, sale price to get 40% profit = $168 Answer

Question (3) A shopkeeper purchases notebooks at $5 for 10 and sells it at $5 for 4, then find his profit percentage.

Solution

Given, Cost price of 10 notebooks = $5

Again given, sale price for 4 notebooks = $5

Thus, sale price of 1 notebook = $5/4 = $1.25

Thus, sale price of 10 notebooks = price of one notebook × 10

= $1.25 × 10 = $12.50

Now, here cost price = $5 and sale price = $12.50

Thus, profit = Sale price – cost price

= $12.50 – $5

= $7.50

Now, On $5 the shopkeeper earns $7.50

Therefore, on $1, earning of shopkeeper = 7.50/5 = $1.5

Therefore, on $100, earning of shopkeeper = $1.5 × 100

= 150%

Thus, earning of shopkeeper = 150% Answer

Alternate method to solve this question on Profit and Loss

Given, Cost price of 10 notebooks = $5

Again given, sale price for 4 notebooks = $5

Thus, sale price of 1 notebook = $5/4 = $1.25

Thus, sale price of 10 notebooks = price of one notebook × 10

= $1.25 × 10 = $12.50

Thus, profit = Sale price – cost price

= $12.50 – $5

= $7.50

Now we know that profit %

= 7.50 × 20 = 150%

Thus, profit = 150% Answer

Alternate method to solve this question on Profit and Loss

Given, Cost price of 10 notebooks = $5

Thus, cost price of 1 notebook = 5/10 = $0.5

Again given, sale price for 4 notebooks = $5

Thus, sale price of 1 notebook = $5/4 = $1.25

Thus, profit on 1 notebook = Sale price of 1 notebook – Cost price of 1 notebook

= $1.25 – $0.5 = $0.75

Now, on $0.5 earning of shopkeeper = $0.75

Therefore, on 1, earning of shopkeeper = 0.75/0.5 = 1.5

Thus, on 100, earning of shopkeeper = 1.5 × 100 = 150%

Thus, profit = 150% Answer

Alternate method to solve this question on Profit and Loss

Given, Cost price of 10 notebooks = $5

Thus, cost price of 1 notebook = 5/10 = $0.5

Again given, sale price for 4 notebooks = $5

Thus, sale price of 1 notebook = $5/4 = $1.25

Thus, profit on 1 notebook = Sale price of 1 notebook – Cost price of 1 notebook

= $1.25 – $0.5 = $0.75

Now, on $0.5 earning of shopkeeper = $0.75

Therefore, on 1, earning of shopkeeper = 0.75/0.5 = 1.5

Now we know that profit %

= 1.5 × 100 = 150%

Thus, profit = 150% Answer

Question (4) A vendor purchased 10 dozen bananas for $3 per dozen. Due to bad weather bananas started getting rotten. If in order to reduce his loss, he sold them 20 cents per banana, then find his loss percent.

Solution

Given, cost price of banana = $3 per dozen

Selling price = 20 cent per banana

Therefore, price for 12 (one dozen) banana = 20 × 12

= 240 cents = 240/100 = $2.4

Thus, selling price per dozen = $2.4

Thus, loss per dozen = cost price – sale price

= $3.00 – $2.40 = $0.60

Now, since in $3.00 loss = $0.60

Therefore, in $1.00 loss = 0.60/3.00 = 0.2

Thus, in $100 loss = 0.2 × 100 = 20%

Thus, loss = 20% Answer

Alternate method to solve this question of Profit and Loss

Given, cost price of banana = $3 per dozen

Total banana purchased = 10 dozens

Thus, total cost price = $3 × 10 = $30

Selling price = 20 cent per banana

Therefore, sale price for 12 (one dozen) banana = 20 × 12

= 240 cents = 240/100 = $2.4

Thus, selling price per dozen = $2.4

Thus, total sale price for 10 dozens of bananas

= $2.4 × 10 = $24

Thus, loss per dozen = cost price – sale price

= $30 – $24 = $6

Now, since in $30 loss = $6

Therefore, in $1.00 loss = 6/30 = 0.2

Thus, in $100 loss = 0.2 × 100 = 20%

Thus, loss = 20% Answer

Alternate method to solve this question of Profit and Loss

Given, cost price of banana = $3 per dozen

Total banana purchased = 10 dozens

Thus, total cost price = $3 × 10 = $30

Selling price = 20 cent per banana

Therefore, sale price for 12 (one dozen) banana = 20 × 12

= 240 cents = 240/100 = $2.4

Thus, selling price per dozen = $2.4

Thus, total sale price for 10 dozens of bananas

= $2.4 × 10 = $24

Thus, loss per dozen = cost price – sale price

= $30 – $24 = $6

Now, we know that,

Thus, loss = 20% Answer

Question (5) A vendor purchased 50 dozen bananas for $3 per dozen. He started selling $4 per dozen and could sell only 20 dozen in the first day. After that due to bad weather bananas started getting rotten. If in order to reduce his loss, he sold them $2.5 per dozen, then find his loss or profit percent.

Solution

Given, cost price per dozen = $3

Total banana purchased = 50 dozens

Thus, total cost price = $3 × 50 = $150

Sale price for 20 dozen = $4 per dozen

Thus, total sale price for 20 dozen = $4 × 20 = $80

Sale price for rest 30 dozen = $2.5 per dozen

Thus, total sale price for 30 dozen = $2.5 × 30 = $75

Thus, total sale price for 50 dozen = sale price for 20 dozen + sale price for 30 dozen

= $80 + $75 = $155

Here, since sale price is greater than the cost price, thus in this deal vendor gets profit.

Now, Profit = sale price – cost price

= $150 – $155 = $5

⇒ Profit = $5

Now, since in $150 the profit of vendor = $5

Therefore, in $1 the profit of vendor = 5/150

Thus, in $100, the profit of vendor

= 3.33 %

Thus, profit = 3.33% Answer

Alternate method to solve this question of Profit and Loss

Here total cost price = $150

And, total sale price = $155

Thus, profit = sale price – cost price

= $155 – 150 = $5

⇒ Profit = $5

Now, we know that,

Thus, profit = 3.33% Answer

Question (6) A shopkeeper purchased 20 bags of rice for $50 per bag. He sold 10 bags of rice at the rate of $3 per kilogram and rest of the rice at the rate of $2 per kilogram. If one bag contains 25 kg of rice, then find his loss or profit percent.

Solution

Given, cost price of 20 bags = $50 per bag

Thus, total cost price = $50 × 20 = $1000

Quantity of rice in one bag = 25 kg

Sale price for 10 bags = $3 per kilogram

Thus, sale price for one bag (25 kg) @$3 per kg

= $3 × 25

= $75

Thus, sale price for 10 bags = $75 × 10 = $750

Again given, sale price of rest 10 bags = $2 per kilogram

Thus, sale price for 1 bag @$2 per kilogram = $2 × 25 = $50

Thus, sale price for 10 bags = $50 × 10 = $500

Now, total sale price = sale price for 10 bags @ $3 per kg + sale price for rest 10 bags @ $2 per kg

= $750 + $500 = $1250

⇒ Total sale price = $1250

Here, total cost price is $100 and total sale price is $1250, thus in this selling shopkeeper earns profit.

Now, profit = Sale price – Cost price

= $1250 – $1000 = $250

Now, since in $1000, the profit = $250

Therefore, in $1, the profit

= $250/$1000 = 1/4 = 0.25

Therefore, in $100, the profit = 0.25 × 100 = 25%

Thus, profit = 25%

Alternate method to solve this question of Profit and Loss

Here total cost price = $100

And, total sale price = $1250

Thus, profit = sale price – cost price

= $1250 – 1000 = $250

⇒ Profit = $250

Now, we know that

Thus, profit = 25% Answer

Question (7) A shopkeeper purchased 10 boxes of chocolates for $12 per box. He sold 300 chocolates at the rate of 20 cents per chocolate, 500 chocolates at the rate of 30 cents per chocolate and rest of them at the rate of 45 cents per chocolate. If each box contains 100 chocolates, then find his loss or gain percent.

Solution

Given, total number of boxes = 10

Cost price per box = $12

Thus, total cost price = $12 × 10 = $120

Number of chocolate each box contains = 100

Therefore, total number of chocolates = 10 × 100 = 1000

Calculation of Selling price of 300 chocolates sold for 20 cents per chocolate

Again given 300 chocolates has been sold at the rate of 20 cents per chocolate.

Thus, Selling price for 300 chocolates at the rate of 20 cents per chocolate

= 300 × 20

= 6000 cents

= 6000/100 = $60

Calculation of Selling price of 500 chocolates sold for 30 cents per chocolate

Again given 500 chocolates has been sold at the rate of 30 cents per chocolate.

Thus, Selling price for 500 chocolates at the rate of 30 cents per chocolate

= 500 × 30

= 15000 cents

= 15000/100 = $150

Calculation of Selling price of rest of the chocolates that sold for 45 cents per chocolate

Again given, rest of chocolates has been sold for 45 cents per chocolate

Now total chocolate left = total number of chocolate – total chocolate sold

= 1000 – (300 + 500)

= 1000 – 800 = 200

Thus, chocolates sold for 45 cents per chocolate = 200

Thus, selling price of 200 chocolates that sold for 45 cents per chocolate

= 45 × 200 = 9000 cents

= 9000/100 = $90

Now, total selling price = selling price of 300 chocolate sold for 20 cents per chocolate + selling price of 500 chocolate sold for 30 cents per chocolate + selling price of 200 chocolate sold for 45 cents per chocolate

= $60 + $150 + $90 = $300

Thus, total selling price = $300

And total cost price = $120

Here, since selling price is greater than the cost price, thus in this deal the shopkeeper earns profit.

Now, profit = sale price – cost price

= $300 – $120 = $180

Now, we know that

= 150%

Thus, profit = 150% Answer

Question (8) A vendor purchased bananas for $3 per dozen. To make a profit of 40% what will be the selling price per banana?

Solution

Given, cost price = $3 per dozen

Profit = 40%

Selling price per banana = ?

Now, 40% of $3

= 0.4 × $3 = $1.2

Thus, selling price per dozen after 40% profit

= Cost price + profit

= $3 + $1.20 = $4.20

We know that, one dozen = 12 piece

Thus, selling price for one banana = selling price for one dozen/12

= $4.20/12 = $0.35

Thus, sale price per banana after 40% profit = $0.35 or 35 cents Answer

Alternate method to solve this question of Profit and Loss

Given, cost price = $3 per dozen

Profit = 40%

Selling price per banana = ?

Now, since cost price per dozen = $3

Thus, cost price per banana = $3/12 = $0.25

Now, sale price per banana to earn 40% profit

= 140% of cost price

= $0.35

Thus, sale price per banana to earn 40% profit = $0.35 or 35 cents Answer