Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.

Correct Answer  2.08%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 49 articles = $1

The Sale Price (SP) for 48 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 49 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₉

∵ The Sale Price (SP) for 48 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₈

Calculation of profit

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

= ¹/₄₈ – ¹/₄₉

= ^{49 – 48}/₂₃₅₂

⇒ Profit = ¹/₂₃₅₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₉, the the profit = ¹/₂₃₅₂

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

= ^{1/₂₃₅₂}/_¹/49

= ¹/₂₃₅₂ × ⁴⁹/₁

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

= ¹/₂₃₅₂ × ⁴⁹/₁ × 100

= ^{1 × 49 × 100}/_{2352 × 1}

= ⁴⁹⁰⁰/₂₃₅₂ = 2.08

Thus, Profit = 2.08% 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 49 articles = $1

And, the Sale Price (SP) of 48 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 49 and 48 = 2352

Now, Let total number of articles purchased = 2352

Here, since the Cost Price of 49 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₉

Therefore, the Cost Price of 2352 articles

And, since the Sale Price of 48 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₈

Therefore, the Sale Price of 2352 articles

= ¹/₄₈ × 2352 = $49

⇒ The Sale Price (SP) of 2352 articles = $49

Now, the Cost Price (CP) of 2352 articles = $48

And, the Sale Price (SP) of 2352 articles = $49

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)

= 49 – 48 = 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}/₄₈

= ¹⁰⁰/₄₈ = 2.08

Thus, profit = 2.08% Answer

Similar Questions

(1) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?

(2) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(3) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(4) James loses 66% by selling an article for $1074.40. For how much should he sell it to get a profit of 65%?

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

(6) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(7) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(8) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

(9) A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.

(10) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.