Profit And Loss
Math MCQs

Question :    Mr. Jojo buys 30 articles for $1 and sells 29 articles for $1. Find the profit in percent.

Correct Answer  3.45%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 30 articles = $1

The Sale Price (SP) for 29 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 30 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₀

∵ The Sale Price (SP) for 29 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₉

Calculation of profit

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

= ¹/₂₉ – ¹/₃₀

= ^{30 – 29}/₈₇₀

⇒ Profit = ¹/₈₇₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₀, the the profit = ¹/₈₇₀

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

= ^1/₈₇₀/_¹/30

= ¹/₈₇₀ × ³⁰/₁

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

= ¹/₈₇₀ × ³⁰/₁ × 100

= ^{1 × 30 × 100}/_{870 × 1}

= ³⁰⁰⁰/₈₇₀ = 3.45

Thus, Profit = 3.45% 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 30 articles = $1

And, the Sale Price (SP) of 29 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 30 and 29 = 870

Now, Let total number of articles purchased = 870

Here, since the Cost Price of 30 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₀

Therefore, the Cost Price of 870 articles

And, since the Sale Price of 29 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₉

Therefore, the Sale Price of 870 articles

= ¹/₂₉ × 870 = $30

⇒ The Sale Price (SP) of 870 articles = $30

Now, the Cost Price (CP) of 870 articles = $29

And, the Sale Price (SP) of 870 articles = $30

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)

= 30 – 29 = 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}/₂₉

= ¹⁰⁰/₂₉ = 3.45

Thus, profit = 3.45% Answer

Similar Questions

(1) 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%?

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

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

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

(5) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(6) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

(7) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

(8) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10

(9) Find the cost price, if a trader gets a loss of 69% by selling 12 bags of fruit for $4219.10

(10) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?