Profit And Loss
Math MCQs

Question :    If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

Correct Answer  6910

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) = $31095

And, the profit = 350%

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 + 350} × 31095

= ^{100 × 31095}/₄₅₀

= ^3109500/₄₅₀ = 6910

Thus, the Cost Price (CP) = $6910 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 = 350%

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

= 350% of m

= 350% × m

= ³⁵⁰/₁₀₀ × m

⇒ Profit = ^{350 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 31095 = m + ^{350 m}/₁₀₀

⇒ 31095 = ^{100 m + 350 m}/₁₀₀

⇒ 31095 = ^{450 m}/₁₀₀

After cross multiplication, we get

31095 × 100 = 450 m

⇒ 450 m = 31095 × 100

⇒ m = ^{31095 × 100}/₄₅₀

⇒ m = ^3109500/₄₅₀ = 6910

⇒ m = 6910

Thus, the Cost Price (CP) = $6910 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) = $31095

And, the profit = 350%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 350% of 100 = 350

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

⇒ Sale Price (SP) = 100 + 350

⇒ Sale Price (SP) = 450

∵ If the Sale Price (SP) is 450, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₅₀

∴ If the Sale Price (SP) is 31095, then the Cost Price (CP)

= ¹⁰⁰/₄₅₀ × 31095

= ^{100 × 31095}/₄₅₀

= ^3109500/₄₅₀ = 6910

Thus, the Cost Price (CP) = $6910 Answer

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

Given, the sale price (SP) = $31095

And, the profit = 350%

Then, the Cost Price (CP) = ?

SP = 450% of CP

⇒ SP = ⁴⁵⁰/₁₀₀ × CP

⇒ 31095 = ^{450 CP}/₁₀₀

After cross multiplication

⇒ 31095 × 100 = 450 CP

⇒ 450 CP = 31095 × 100

⇒ CP = ^{31095 × 100}/₄₅₀

⇒ CP = ^3109500/₄₅₀ = 6910

⇒ CP = $6910 Answer

Similar Questions

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(2) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

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

(4) Find the cost price, if a trader gets a loss of 58% by selling two TV sets for $4792.20

(5) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.

(6) Jojo loses 36% by selling an article for $1062.40. For how much should he sell it to get a profit of 35%?

(7) 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%?

(8) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

(9) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(10) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?