Profit And Loss
Math MCQs

Question :    If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

Correct Answer  1.67%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 61 articles = $1

The Sale Price (SP) for 60 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 61 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₁

∵ The Sale Price (SP) for 60 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₀

Calculation of profit

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

= ¹/₆₀ – ¹/₆₁

= ^{61 – 60}/₃₆₆₀

⇒ Profit = ¹/₃₆₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₁, the the profit = ¹/₃₆₆₀

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

= ^{1/₃₆₆₀}/_¹/61

= ¹/₃₆₆₀ × ⁶¹/₁

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

= ¹/₃₆₆₀ × ⁶¹/₁ × 100

= ^{1 × 61 × 100}/_{3660 × 1}

= ⁶¹⁰⁰/₃₆₆₀ = 1.67

Thus, Profit = 1.67% 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 61 articles = $1

And, the Sale Price (SP) of 60 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 61 and 60 = 3660

Now, Let total number of articles purchased = 3660

Here, since the Cost Price of 61 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₁

Therefore, the Cost Price of 3660 articles

And, since the Sale Price of 60 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₀

Therefore, the Sale Price of 3660 articles

= ¹/₆₀ × 3660 = $61

⇒ The Sale Price (SP) of 3660 articles = $61

Now, the Cost Price (CP) of 3660 articles = $60

And, the Sale Price (SP) of 3660 articles = $61

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)

= 61 – 60 = 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}/₆₀

= ¹⁰⁰/₆₀ = 1.67

Thus, profit = 1.67% Answer

Similar Questions

(1) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

(2) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30

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

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

(5) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?

(6) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(7) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

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

(9) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(10) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?