Profit And Loss
Math MCQs

Question :    In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

Correct Answer  1410

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) = $2467.5

And, the profit = 75%

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 + 75} × 2467.5

= ^{100 × 2467.5}/₁₇₅

= ²⁴⁶⁷⁵⁰/₁₇₅ = 1410

Thus, the Cost Price (CP) = $1410 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 = 75%

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

= 75% of m

= 75% × m

= ⁷⁵/₁₀₀ × m

⇒ Profit = ^{75 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 2467.5 = m + ^{75 m}/₁₀₀

⇒ 2467.5 = ^{100 m + 75 m}/₁₀₀

⇒ 2467.5 = ^{175 m}/₁₀₀

After cross multiplication, we get

2467.5 × 100 = 175 m

⇒ 175 m = 2467.5 × 100

⇒ m = ^{2467.5 × 100}/₁₇₅

⇒ m = ²⁴⁶⁷⁵⁰/₁₇₅ = 1410

⇒ m = 1410

Thus, the Cost Price (CP) = $1410 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) = $2467.5

And, the profit = 75%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 75% of 100 = 75

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

⇒ Sale Price (SP) = 100 + 75

⇒ Sale Price (SP) = 175

∵ If the Sale Price (SP) is 175, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₇₅

∴ If the Sale Price (SP) is 2467.5, then the Cost Price (CP)

= ¹⁰⁰/₁₇₅ × 2467.5

= ^{100 × 2467.5}/₁₇₅

= ²⁴⁶⁷⁵⁰/₁₇₅ = 1410

Thus, the Cost Price (CP) = $1410 Answer

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

Given, the sale price (SP) = $2467.5

And, the profit = 75%

Then, the Cost Price (CP) = ?

SP = 175% of CP

⇒ SP = ¹⁷⁵/₁₀₀ × CP

⇒ 2467.5 = ^{175 CP}/₁₀₀

After cross multiplication

⇒ 2467.5 × 100 = 175 CP

⇒ 175 CP = 2467.5 × 100

⇒ CP = ^{2467.5 × 100}/₁₇₅

⇒ CP = ²⁴⁶⁷⁵⁰/₁₇₅ = 1410

⇒ CP = $1410 Answer

Similar Questions

(1) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(2) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?

(3) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.

(4) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

(5) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(6) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(7) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

(8) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(9) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

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