Profit And Loss
Math MCQs

Question :    If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

Correct Answer  $4210

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) = $3283.8

And, the loss = 22%

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 – 22} × 3283.8

= ¹⁰⁰/₇₈ × 3283.8

= ³²⁸³⁸⁰/₇₈ = 4210

Thus, the Cost Price (CP) = $4210 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 = 22%

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

= 22% of m

= 22% × m

= ²/₁₀₀ × m

⇒ loss = ^{22 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

⇒ 3283.8 = m – ^{22 m}/₁₀₀

⇒ 3283.8 = ^{100 m – 22 m}/₁₀₀

⇒ 3283.8 = ^{78 m}/₁₀₀

After cross multiplication, we get

3283.8 × 100 = 78 m

⇒ 78 m = 3283.8 × 100

⇒ m = ^{3283.8 × 100}/₇₈

⇒ m = ^{3283.8 × 100}/₇₈

⇒ m = ³²⁸³⁸⁰/₇₈ = 4210

Thus, the Cost Price (CP) = $4210 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) = $3283.8

And, the loss = 22%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 22% of 100 = 22

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

⇒ Sale Price (SP) = 100 – 22

⇒ Sale Price (SP) = 78

∵ If the Sale Price (SP) is 78, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₇₈

∴ If the Sale Price (SP) is 3283.8, then the Cost Price (CP)

= ¹⁰⁰/₇₈ × 3283.8

= ^{100 × 3283.8}/₇₈ = 4210

Thus, the Cost Price (CP) = $4210 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) = $3283.8

And, the loss = 22%

Then, the Cost Price (CP) = ?

SP = 78% of CP

⇒ SP = 78% of CP

⇒ 3283.8 = ⁷⁸/₁₀₀ × CP

⇒ 3283.8 = ^{78 CP}/₁₀₀

After cross multiplication

⇒ 3283.8 × 100 = 78 CP

⇒ 78 CP = 3283.8 × 100

⇒ CP = ^{3283.8 × 100}/₇₈

⇒ CP = ³²⁸³⁸⁰/₇₈ = 4210

⇒ CP = $4210 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 = 22%

And the Sale Price = $3283.8

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

⇒ 100 – 22% of the Cost Price = $3283.8

⇒ 78% of the Cost Price = 3283.8

Therefore, 1% of the Cost Price = ^3283.8/₇₈

Thus, 100% the Cost Price = ^3283.8/₇₈ × 100

= ³²⁸³⁸⁰/₇₈ = 4210

Thus the Cost Price (CP) = $4210 Answer

Similar Questions

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(2) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?

(3) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(4) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(5) Mr. Steven loses 93% by selling an article for $315.70. For how much should he sell it to get a profit of 92%?

(6) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

(7) A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?

(8) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(9) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(10) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.