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

(2) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(3) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(4) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

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

(6) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(7) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(8) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

(9) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

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