Profit And Loss
Math MCQs

Question :    If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

Correct Answer  $2410

Solution & 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) = $2096.7

And, the loss = 13%

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 – 13} × 2096.7

= ¹⁰⁰/₈₇ × 2096.7

= ²⁰⁹⁶⁷⁰/₈₇ = 2410

Thus, the Cost Price (CP) = $2410 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 = 13%

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

= 13% of m

= 13% × m

= ²/₁₀₀ × m

⇒ loss = ^{13 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

⇒ 2096.7 = m – ^{13 m}/₁₀₀

⇒ 2096.7 = ^{100 m – 13 m}/₁₀₀

⇒ 2096.7 = ^{87 m}/₁₀₀

After cross multiplication, we get

2096.7 × 100 = 87 m

⇒ 87 m = 2096.7 × 100

⇒ m = ^{2096.7 × 100}/₈₇

⇒ m = ^{2096.7 × 100}/₈₇

⇒ m = ²⁰⁹⁶⁷⁰/₈₇ = 2410

Thus, the Cost Price (CP) = $2410 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) = $2096.7

And, the loss = 13%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 13% of 100 = 13

Thus, Sale Price (SP) = Cost Price (CP) – loss

⇒ Sale Price (SP) = 100 – 13

⇒ Sale Price (SP) = 87

∵ If the Sale Price (SP) is 87, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₈₇

∴ If the Sale Price (SP) is 2096.7, then the Cost Price (CP)

= ¹⁰⁰/₈₇ × 2096.7

= ^{100 × 2096.7}/₈₇ = 2410

Thus, the Cost Price (CP) = $2410 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) = $2096.7

And, the loss = 13%

Then, the Cost Price (CP) = ?

SP = 87% of CP

⇒ SP = 87% of CP

⇒ 2096.7 = ⁸⁷/₁₀₀ × CP

⇒ 2096.7 = ^{87 CP}/₁₀₀

After cross multiplication

⇒ 2096.7 × 100 = 87 CP

⇒ 87 CP = 2096.7 × 100

⇒ CP = ^{2096.7 × 100}/₈₇

⇒ CP = ²⁰⁹⁶⁷⁰/₈₇ = 2410

⇒ CP = $2410 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 = 13%

And the Sale Price = $2096.7

This means 100 – loss% of the Cost Price = Sale Price

⇒ 100 – 13% of the Cost Price = $2096.7

⇒ 87% of the Cost Price = 2096.7

Therefore, 1% of the Cost Price = ^2096.7/₈₇

Thus, 100% the Cost Price = ^2096.7/₈₇ × 100

= ²⁰⁹⁶⁷⁰/₈₇ = 2410

Thus the Cost Price (CP) = $2410 Answer

Similar Questions

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(2) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

(3) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(4) Mr. Oliver loses 82% by selling an article for $712.80. For how much should he sell it to get a profit of 81%?

(5) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

(6) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

(7) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(8) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

(9) A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?

(10) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.