Profit And Loss
Math MCQs

Question :    Find the cost price if a broker earned 375% while dealing a house for $35197.50

Correct Answer  7410

Solution & Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $35197.5

And, the profit = 375%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 375} × 35197.5

= ^{100 × 35197.5}/₄₇₅

= ^3519750/₄₇₅ = 7410

Thus, the Cost Price (CP) = $7410 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 375%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 375% of m

= 375% × m

= ³⁷⁵/₁₀₀ × m

⇒ Profit = ^{375 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 35197.5 = m + ^{375 m}/₁₀₀

⇒ 35197.5 = ^{100 m + 375 m}/₁₀₀

⇒ 35197.5 = ^{475 m}/₁₀₀

After cross multiplication, we get

35197.5 × 100 = 475 m

⇒ 475 m = 35197.5 × 100

⇒ m = ^{35197.5 × 100}/₄₇₅

⇒ m = ^3519750/₄₇₅ = 7410

⇒ m = 7410

Thus, the Cost Price (CP) = $7410 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $35197.5

And, the profit = 375%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 375% of 100 = 375

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 375

⇒ Sale Price (SP) = 475

∵ If the Sale Price (SP) is 475, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₇₅

∴ If the Sale Price (SP) is 35197.5, then the Cost Price (CP)

= ¹⁰⁰/₄₇₅ × 35197.5

= ^{100 × 35197.5}/₄₇₅

= ^3519750/₄₇₅ = 7410

Thus, the Cost Price (CP) = $7410 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $35197.5

And, the profit = 375%

Then, the Cost Price (CP) = ?

SP = 475% of CP

⇒ SP = ⁴⁷⁵/₁₀₀ × CP

⇒ 35197.5 = ^{475 CP}/₁₀₀

After cross multiplication

⇒ 35197.5 × 100 = 475 CP

⇒ 475 CP = 35197.5 × 100

⇒ CP = ^{35197.5 × 100}/₄₇₅

⇒ CP = ^3519750/₄₇₅ = 7410

⇒ CP = $7410 Answer

Similar Questions

(1) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(2) A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?

(3) Find the cost price, if a trader gets a loss of 12% by selling some of his stock of fruits for $1944.80. Find the cost price of those stock.

(4) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.

(5) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(6) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(7) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724

(8) Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?

(9) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

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