Question:
If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.
Correct Answer
$6410
Solution And Explanation
Solution
Finding the cost price if the sale price and loss percent are known
The cost price (CP) can be found using the formula, algebraic method, shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want. Here the five methods to solve this problem have been given.
Method (1) Using Formula
Finding the cost price using the formula when the sale price and loss percent are known
Given, the sale price (SP) = $4294.7
And, the loss = 33%
Then, the Cost Price (CP) = ?
Formula to find the cost price when the sale price and loss percent are known
Cost Price (CP) = 100/100 – gain% × SP
Thus, the Cost Price (CP)
= 100/100 – 33 × 4294.7
= 100/67 × 4294.7
= 429470/67 = 6410
Thus, the Cost Price (CP) = $6410 Answer
Method (2) Algebraic Method
Finding the cost price (CP) using the Algebraic Method when the Sale Price (SP) and the loss percent are given
Let the Cost Price (CP) = m
Here given loss = 33%
Calculation of loss
The loss and/or profit is calculated on the cost price (CP)
Formula to find the loss when the Cost Price and the Loss% are given
Loss = loss% of CP
Thus, loss on the cost price of m
= Loss% of m
= 33% of m
= 33% × m
= 2/100 × m
⇒ loss = 33 m/100
Calculation of Cost Price (CP)
Formula to find the Sale Price (SP) when the Cost Price (CP) and the Loss are given
Sale Price (SP) = Cost Price (CP) – Loss
⇒ 4294.7 = m – 33 m/100
⇒ 4294.7 = 100 m – 33 m/100
⇒ 4294.7 = 67 m/100
After cross multiplication, we get
4294.7 × 100 = 67 m
⇒ 67 m = 4294.7 × 100
⇒ m = 4294.7 × 100/67
⇒ m = 4294.7 × 100/67
⇒ m = 429470/67 = 6410
Thus, the Cost Price (CP) = $6410 Answer
Method (3) Unitary Method
Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the loss percent are given
Given, the sale price (SP) = $4294.7
And, the loss = 33%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 33% of 100 = 33
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 33
⇒ Sale Price (SP) = 67
∵ If the Sale Price (SP) is 67, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/67
∴ If the Sale Price (SP) is 4294.7, then the Cost Price (CP)
= 100/67 × 4294.7
= 100 × 4294.7/67 = 6410
Thus, the Cost Price (CP) = $6410 Answer
Method (4) Shortcut Method (1)
Shortcut Method to find Cost Price (CP) when SP and loss percent are known
Given, the sale price (SP) = $4294.7
And, the loss = 33%
Then, the Cost Price (CP) = ?
SP = 67% of CP
⇒ SP = 67% of CP
⇒ 4294.7 = 67/100 × CP
⇒ 4294.7 = 67 CP/100
After cross multiplication
⇒ 4294.7 × 100 = 67 CP
⇒ 67 CP = 4294.7 × 100
⇒ CP = 4294.7 × 100/67
⇒ CP = 429470/67 = 6410
⇒ CP = $6410 Answer
Method (5) Shortcut Method (2)
Shortcut Method (2) to find Cost Price (CP) when SP and loss percent are known
Here loss and the Sale Price are given and the Cost Price is to find
Here as given, the loss = 33%
And the Sale Price = $4294.7
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 33% of the Cost Price = $4294.7
⇒ 67% of the Cost Price = 4294.7
Therefore, 1% of the Cost Price = 4294.7/67
Thus, 100% the Cost Price = 4294.7/67 × 100
= 429470/67 = 6410
Thus the Cost Price (CP) = $6410 Answer
Similar Questions
(1) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?
(2) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?
(3) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.
(4) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40
(5) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.
(6) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?
(7) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.
(8) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?
(9) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?
(10) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?