Profit And Loss
Math MCQs

Question :    If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.

Correct Answer  1.35%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 75 articles = $1

The Sale Price (SP) for 74 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 75 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₅

∵ The Sale Price (SP) for 74 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₄

Calculation of profit

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

= ¹/₇₄ – ¹/₇₅

= ^{75 – 74}/₅₅₅₀

⇒ Profit = ¹/₅₅₅₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₅, the the profit = ¹/₅₅₅₀

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

= ^{1/₅₅₅₀}/_¹/75

= ¹/₅₅₅₀ × ⁷⁵/₁

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

= ¹/₅₅₅₀ × ⁷⁵/₁ × 100

= ^{1 × 75 × 100}/_{5550 × 1}

= ⁷⁵⁰⁰/₅₅₅₀ = 1.35

Thus, Profit = 1.35% 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 75 articles = $1

And, the Sale Price (SP) of 74 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 75 and 74 = 5550

Now, Let total number of articles purchased = 5550

Here, since the Cost Price of 75 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₅

Therefore, the Cost Price of 5550 articles

And, since the Sale Price of 74 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₄

Therefore, the Sale Price of 5550 articles

= ¹/₇₄ × 5550 = $75

⇒ The Sale Price (SP) of 5550 articles = $75

Now, the Cost Price (CP) of 5550 articles = $74

And, the Sale Price (SP) of 5550 articles = $75

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)

= 75 – 74 = 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}/₇₄

= ¹⁰⁰/₇₄ = 1.35

Thus, profit = 1.35% Answer

Similar Questions

(1) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?

(2) Find the cost price, if a trader gets a loss of 54% by selling 100 bags of mobile covers for $4880.60

(3) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

(4) 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%?

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

(6) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90

(7) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

(8) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(9) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?

(10) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90