Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

Correct Answer  $5810

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) = $4067

And, the loss = 30%

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 – 30} × 4067

= ¹⁰⁰/₇₀ × 4067

= ⁴⁰⁶⁷⁰⁰/₇₀ = 5810

Thus, the Cost Price (CP) = $5810 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 = 30%

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

= 30% of m

= 30% × m

= ²/₁₀₀ × m

⇒ loss = ^{30 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

⇒ 4067 = m – ^{30 m}/₁₀₀

⇒ 4067 = ^{100 m – 30 m}/₁₀₀

⇒ 4067 = ^{70 m}/₁₀₀

After cross multiplication, we get

4067 × 100 = 70 m

⇒ 70 m = 4067 × 100

⇒ m = ^{4067 × 100}/₇₀

⇒ m = ^{4067 × 100}/₇₀

⇒ m = ⁴⁰⁶⁷⁰⁰/₇₀ = 5810

Thus, the Cost Price (CP) = $5810 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) = $4067

And, the loss = 30%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 30% of 100 = 30

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

⇒ Sale Price (SP) = 100 – 30

⇒ Sale Price (SP) = 70

∵ If the Sale Price (SP) is 70, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₇₀

∴ If the Sale Price (SP) is 4067, then the Cost Price (CP)

= ¹⁰⁰/₇₀ × 4067

= ^{100 × 4067}/₇₀ = 5810

Thus, the Cost Price (CP) = $5810 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) = $4067

And, the loss = 30%

Then, the Cost Price (CP) = ?

SP = 70% of CP

⇒ SP = 70% of CP

⇒ 4067 = ⁷⁰/₁₀₀ × CP

⇒ 4067 = ^{70 CP}/₁₀₀

After cross multiplication

⇒ 4067 × 100 = 70 CP

⇒ 70 CP = 4067 × 100

⇒ CP = ^{4067 × 100}/₇₀

⇒ CP = ⁴⁰⁶⁷⁰⁰/₇₀ = 5810

⇒ CP = $5810 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 = 30%

And the Sale Price = $4067

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

⇒ 100 – 30% of the Cost Price = $4067

⇒ 70% of the Cost Price = 4067

Therefore, 1% of the Cost Price = ⁴⁰⁶⁷/₇₀

Thus, 100% the Cost Price = ⁴⁰⁶⁷/₇₀ × 100

= ⁴⁰⁶⁷⁰⁰/₇₀ = 5810

Thus the Cost Price (CP) = $5810 Answer

Similar Questions

(1) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(2) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(3) Peter loses 32% by selling an article for $992.80. For how much should he sell it to get a profit of 31%?

(4) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(5) If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.

(6) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

(7) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(8) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(9) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(10) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.