Profit And Loss
Math MCQs

Question :    How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

Correct Answer  3.03%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 34 articles = $1

The Sale Price (SP) for 33 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 34 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₄

∵ The Sale Price (SP) for 33 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₃

Calculation of profit

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

= ¹/₃₃ – ¹/₃₄

= ^{34 – 33}/₁₁₂₂

⇒ Profit = ¹/₁₁₂₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₄, the the profit = ¹/₁₁₂₂

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

= ^{1/₁₁₂₂}/_¹/34

= ¹/₁₁₂₂ × ³⁴/₁

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

= ¹/₁₁₂₂ × ³⁴/₁ × 100

= ^{1 × 34 × 100}/_{1122 × 1}

= ³⁴⁰⁰/₁₁₂₂ = 3.03

Thus, Profit = 3.03% 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 34 articles = $1

And, the Sale Price (SP) of 33 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 34 and 33 = 1122

Now, Let total number of articles purchased = 1122

Here, since the Cost Price of 34 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₄

Therefore, the Cost Price of 1122 articles

And, since the Sale Price of 33 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₃

Therefore, the Sale Price of 1122 articles

= ¹/₃₃ × 1122 = $34

⇒ The Sale Price (SP) of 1122 articles = $34

Now, the Cost Price (CP) of 1122 articles = $33

And, the Sale Price (SP) of 1122 articles = $34

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)

= 34 – 33 = 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}/₃₃

= ¹⁰⁰/₃₃ = 3.03

Thus, profit = 3.03% Answer

Similar Questions

(1) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

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

(3) Find the cost price, if a trader gets a loss of 46% by selling 500 kg rice for $4865.40

(4) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

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

(6) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

(7) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

(8) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(9) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

(10) What will be the cost price if Peter eans a profit of 15% by selling a scooty for $241.5?