Profit And Loss
Math MCQs

Question :    What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

Correct Answer  1.45%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 70 articles = $1

The Sale Price (SP) for 69 articles = $1

Thus, Profit percent = ?

Unitary Method to find the profit when Cost Price and Sale Price are given

∵ The Cost Price (CP) for 70 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₀

∵ The Sale Price (SP) for 69 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₉

Calculation of profit

Profit = Sale Price (SP) – Cost Price (CP)

= ¹/₆₉ – ¹/₇₀

= ^{70 – 69}/₄₈₃₀

⇒ Profit = ¹/₄₈₃₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₀, the the profit = ¹/₄₈₃₀

∴ When the Cost Price (CP) is 1, then the profit

= ^{1/₄₈₃₀}/_¹/70

= ¹/₄₈₃₀ × ⁷⁰/₁

∴ When the Cost Price (CP) is 100, then the profit

= ¹/₄₈₃₀ × ⁷⁰/₁ × 100

= ^{1 × 70 × 100}/_{4830 × 1}

= ⁷⁰⁰⁰/₄₈₃₀ = 1.45

Thus, Profit = 1.45% Answer

Method (2) to find the profit%

Finding the profit percent by taking LCM of the number of articles purchased and sold for the same price

Given, the Cost Price (CP) of 70 articles = $1

And, the Sale Price (SP) of 69 articles = $1

Here, we need to take the LCM of number of articles purchased and sold to make them uniform.

Calculation of the Cost Price (CP) and the Sale Price

The LCM of 70 and 69 = 4830

Now, Let total number of articles purchased = 4830

Here, since the Cost Price of 70 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₀

Therefore, the Cost Price of 4830 articles

And, since the Sale Price of 69 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₉

Therefore, the Sale Price of 4830 articles

= ¹/₆₉ × 4830 = $70

⇒ The Sale Price (SP) of 4830 articles = $70

Now, the Cost Price (CP) of 4830 articles = $69

And, the Sale Price (SP) of 4830 articles = $70

Calculation of the Profit, when the Cost Price (CP) and the Sale Price (SP) are given

Formula to find the profit when the Cost Price (CP) and the Sale Price (SP) are given

Profit = Sale Price (SP) – Cost Price (CP)

= 70 – 69 = 1

⇒ Profit = $1

Calculation of Profit percent using the formula

Formula to calculate the profit percent

Profit percent = ^{Profit × 100}/_{Cost Price}

Thus, profit % = ^{1 × 100}/₆₉

= ¹⁰⁰/₆₉ = 1.45

Thus, profit = 1.45% Answer

Similar Questions

(1) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(2) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(3) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?

(4) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(5) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(6) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(7) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(8) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(9) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(10) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.