Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

Correct Answer  $12210

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) = $4639.8

And, the loss = 62%

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 – 62} × 4639.8

= ¹⁰⁰/₃₈ × 4639.8

= ⁴⁶³⁹⁸⁰/₃₈ = 12210

Thus, the Cost Price (CP) = $12210 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 = 62%

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

= 62% of m

= 62% × m

= ⁶²/₁₀₀ × m

⇒ loss = ^{62 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

⇒ 4639.8 = m – ^{62 m}/₁₀₀

⇒ 4639.8 = ^{100 m – 62 m}/₁₀₀

⇒ 4639.8 = ^{38 m}/₁₀₀

After cross multiplication, we get

4639.8 × 100 = 38 m

⇒ 38 m = 4639.8 × 100

⇒ m = ^{4639.8 × 100}/₃₈

⇒ m = ^{4639.8 × 100}/₃₈

⇒ m = ⁴⁶³⁹⁸⁰/₃₈ = 12210

Thus, the Cost Price (CP) = $12210 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) = $4639.8

And, the loss = 62%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 62% of 100 = 62

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

⇒ Sale Price (SP) = 100 – 62

⇒ Sale Price (SP) = 38

∵ If the Sale Price (SP) is 38, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₈

∴ If the Sale Price (SP) is 4639.8, then the Cost Price (CP)

= ¹⁰⁰/₃₈ × 4639.8

= ^{100 × 4639.8}/₃₈ = 12210

Thus, the Cost Price (CP) = $12210 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) = $4639.8

And, the loss = 62%

Then, the Cost Price (CP) = ?

SP = 38% of CP

⇒ SP = 38% of CP

⇒ 4639.8 = ³⁸/₁₀₀ × CP

⇒ 4639.8 = ^{38 CP}/₁₀₀

After cross multiplication

⇒ 4639.8 × 100 = 38 CP

⇒ 38 CP = 4639.8 × 100

⇒ CP = ^{4639.8 × 100}/₃₈

⇒ CP = ⁴⁶³⁹⁸⁰/₃₈ = 12210

⇒ CP = $12210 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 = 62%

And the Sale Price = $4639.8

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

⇒ 100 – 62% of the Cost Price = $4639.8

⇒ 38% of the Cost Price = 4639.8

Therefore, 1% of the Cost Price = ^4639.8/₃₈

Thus, 100% the Cost Price = ^4639.8/₃₈ × 100

= ⁴⁶³⁹⁸⁰/₃₈ = 12210

Thus the Cost Price (CP) = $12210 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

(2) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(3) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

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

(5) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(6) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(7) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(8) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(9) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(10) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.