Profit And Loss
Math MCQs

Question :    How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

Correct Answer  2.7%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 38 articles = $1

The Sale Price (SP) for 37 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 38 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₈

∵ The Sale Price (SP) for 37 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₇

Calculation of profit

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

= ¹/₃₇ – ¹/₃₈

= ^{38 – 37}/₁₄₀₆

⇒ Profit = ¹/₁₄₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₈, the the profit = ¹/₁₄₀₆

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

= ^{1/₁₄₀₆}/_¹/38

= ¹/₁₄₀₆ × ³⁸/₁

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

= ¹/₁₄₀₆ × ³⁸/₁ × 100

= ^{1 × 38 × 100}/_{1406 × 1}

= ³⁸⁰⁰/₁₄₀₆ = 2.7

Thus, Profit = 2.7% 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 38 articles = $1

And, the Sale Price (SP) of 37 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 38 and 37 = 1406

Now, Let total number of articles purchased = 1406

Here, since the Cost Price of 38 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₈

Therefore, the Cost Price of 1406 articles

And, since the Sale Price of 37 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₇

Therefore, the Sale Price of 1406 articles

= ¹/₃₇ × 1406 = $38

⇒ The Sale Price (SP) of 1406 articles = $38

Now, the Cost Price (CP) of 1406 articles = $37

And, the Sale Price (SP) of 1406 articles = $38

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)

= 38 – 37 = 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}/₃₇

= ¹⁰⁰/₃₇ = 2.7

Thus, profit = 2.7% Answer

Similar Questions

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

(2) Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.

(3) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(4) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(5) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

(6) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(7) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30

(8) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

(9) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.

(10) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?