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) Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20

(2) 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.

(3) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(4) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(5) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(6) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(7) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(8) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(9) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?

(10) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.