Profit And Loss
Math MCQs

Question :    If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

Correct Answer  3.23%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 32 articles = $1

The Sale Price (SP) for 31 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 32 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₂

∵ The Sale Price (SP) for 31 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₁

Calculation of profit

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

= ¹/₃₁ – ¹/₃₂

= ^{32 – 31}/₉₉₂

⇒ Profit = ¹/₉₉₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₂, the the profit = ¹/₉₉₂

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

= ^1/₉₉₂/_¹/32

= ¹/₉₉₂ × ³²/₁

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

= ¹/₉₉₂ × ³²/₁ × 100

= ^{1 × 32 × 100}/_{992 × 1}

= ³²⁰⁰/₉₉₂ = 3.23

Thus, Profit = 3.23% 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 32 articles = $1

And, the Sale Price (SP) of 31 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 32 and 31 = 992

Now, Let total number of articles purchased = 992

Here, since the Cost Price of 32 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₂

Therefore, the Cost Price of 992 articles

And, since the Sale Price of 31 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₁

Therefore, the Sale Price of 992 articles

= ¹/₃₁ × 992 = $32

⇒ The Sale Price (SP) of 992 articles = $32

Now, the Cost Price (CP) of 992 articles = $31

And, the Sale Price (SP) of 992 articles = $32

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)

= 32 – 31 = 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}/₃₁

= ¹⁰⁰/₃₁ = 3.23

Thus, profit = 3.23% Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(2) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(3) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

(4) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.

(5) A dealer gets a loss of 7% by selling an article for $195.30 then, for how much should he sell it to get a profit of 6%?

(6) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80

(7) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

(8) William loses 33% by selling an article for $1011.70. For how much should he sell it to get a profit of 32%?

(9) Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.

(10) Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.