Profit And Loss
Math MCQs

Question :    Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

Correct Answer  3.33%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 31 articles = $1

The Sale Price (SP) for 30 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 31 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₁

∵ The Sale Price (SP) for 30 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₀

Calculation of profit

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

= ¹/₃₀ – ¹/₃₁

= ^{31 – 30}/₉₃₀

⇒ Profit = ¹/₉₃₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₁, the the profit = ¹/₉₃₀

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

= ^1/₉₃₀/_¹/31

= ¹/₉₃₀ × ³¹/₁

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

= ¹/₉₃₀ × ³¹/₁ × 100

= ^{1 × 31 × 100}/_{930 × 1}

= ³¹⁰⁰/₉₃₀ = 3.33

Thus, Profit = 3.33% 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 31 articles = $1

And, the Sale Price (SP) of 30 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 31 and 30 = 930

Now, Let total number of articles purchased = 930

Here, since the Cost Price of 31 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₁

Therefore, the Cost Price of 930 articles

And, since the Sale Price of 30 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₀

Therefore, the Sale Price of 930 articles

= ¹/₃₀ × 930 = $31

⇒ The Sale Price (SP) of 930 articles = $31

Now, the Cost Price (CP) of 930 articles = $30

And, the Sale Price (SP) of 930 articles = $31

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)

= 31 – 30 = 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}/₃₀

= ¹⁰⁰/₃₀ = 3.33

Thus, profit = 3.33% Answer

Similar Questions

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(2) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

(3) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(4) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.

(5) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

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

(7) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

(8) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?

(9) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

(10) 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?