Profit And Loss
Math MCQs

Question :    Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

Correct Answer  $5010

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) = $3707.4

And, the loss = 26%

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 – 26} × 3707.4

= ¹⁰⁰/₇₄ × 3707.4

= ³⁷⁰⁷⁴⁰/₇₄ = 5010

Thus, the Cost Price (CP) = $5010 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 = 26%

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

= 26% of m

= 26% × m

= ²/₁₀₀ × m

⇒ loss = ^{26 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

⇒ 3707.4 = m – ^{26 m}/₁₀₀

⇒ 3707.4 = ^{100 m – 26 m}/₁₀₀

⇒ 3707.4 = ^{74 m}/₁₀₀

After cross multiplication, we get

3707.4 × 100 = 74 m

⇒ 74 m = 3707.4 × 100

⇒ m = ^{3707.4 × 100}/₇₄

⇒ m = ^{3707.4 × 100}/₇₄

⇒ m = ³⁷⁰⁷⁴⁰/₇₄ = 5010

Thus, the Cost Price (CP) = $5010 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) = $3707.4

And, the loss = 26%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 26% of 100 = 26

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

⇒ Sale Price (SP) = 100 – 26

⇒ Sale Price (SP) = 74

∵ If the Sale Price (SP) is 74, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₇₄

∴ If the Sale Price (SP) is 3707.4, then the Cost Price (CP)

= ¹⁰⁰/₇₄ × 3707.4

= ^{100 × 3707.4}/₇₄ = 5010

Thus, the Cost Price (CP) = $5010 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) = $3707.4

And, the loss = 26%

Then, the Cost Price (CP) = ?

SP = 74% of CP

⇒ SP = 74% of CP

⇒ 3707.4 = ⁷⁴/₁₀₀ × CP

⇒ 3707.4 = ^{74 CP}/₁₀₀

After cross multiplication

⇒ 3707.4 × 100 = 74 CP

⇒ 74 CP = 3707.4 × 100

⇒ CP = ^{3707.4 × 100}/₇₄

⇒ CP = ³⁷⁰⁷⁴⁰/₇₄ = 5010

⇒ CP = $5010 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 = 26%

And the Sale Price = $3707.4

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

⇒ 100 – 26% of the Cost Price = $3707.4

⇒ 74% of the Cost Price = 3707.4

Therefore, 1% of the Cost Price = ^3707.4/₇₄

Thus, 100% the Cost Price = ^3707.4/₇₄ × 100

= ³⁷⁰⁷⁴⁰/₇₄ = 5010

Thus the Cost Price (CP) = $5010 Answer

Similar Questions

(1) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(2) Find the cost price if a broker earned 375% while dealing a house for $35197.50

(3) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.

(4) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(5) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

(6) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?

(7) What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?

(8) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.

(9) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.

(10) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.