Profit And Loss
Math MCQs

Question :    How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?

Correct Answer  2.94%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 35 articles = $1

The Sale Price (SP) for 34 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 35 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₅

∵ The Sale Price (SP) for 34 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₄

Calculation of profit

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

= ¹/₃₄ – ¹/₃₅

= ^{35 – 34}/₁₁₉₀

⇒ Profit = ¹/₁₁₉₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₅, the the profit = ¹/₁₁₉₀

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

= ^{1/₁₁₉₀}/_¹/35

= ¹/₁₁₉₀ × ³⁵/₁

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

= ¹/₁₁₉₀ × ³⁵/₁ × 100

= ^{1 × 35 × 100}/_{1190 × 1}

= ³⁵⁰⁰/₁₁₉₀ = 2.94

Thus, Profit = 2.94% 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 35 articles = $1

And, the Sale Price (SP) of 34 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 35 and 34 = 1190

Now, Let total number of articles purchased = 1190

Here, since the Cost Price of 35 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₅

Therefore, the Cost Price of 1190 articles

And, since the Sale Price of 34 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₄

Therefore, the Sale Price of 1190 articles

= ¹/₃₄ × 1190 = $35

⇒ The Sale Price (SP) of 1190 articles = $35

Now, the Cost Price (CP) of 1190 articles = $34

And, the Sale Price (SP) of 1190 articles = $35

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)

= 35 – 34 = 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}/₃₄

= ¹⁰⁰/₃₄ = 2.94

Thus, profit = 2.94% Answer

Similar Questions

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

(2) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

(3) Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%

(4) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

(5) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

(6) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(7) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(8) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(9) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

(10) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?