Profit And Loss
Math MCQs

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

Correct Answer  1.69%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 60 articles = $1

The Sale Price (SP) for 59 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 60 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₀

∵ The Sale Price (SP) for 59 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₉

Calculation of profit

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

= ¹/₅₉ – ¹/₆₀

= ^{60 – 59}/₃₅₄₀

⇒ Profit = ¹/₃₅₄₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₀, the the profit = ¹/₃₅₄₀

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

= ^{1/₃₅₄₀}/_¹/60

= ¹/₃₅₄₀ × ⁶⁰/₁

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

= ¹/₃₅₄₀ × ⁶⁰/₁ × 100

= ^{1 × 60 × 100}/_{3540 × 1}

= ⁶⁰⁰⁰/₃₅₄₀ = 1.69

Thus, Profit = 1.69% 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 60 articles = $1

And, the Sale Price (SP) of 59 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 60 and 59 = 3540

Now, Let total number of articles purchased = 3540

Here, since the Cost Price of 60 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₀

Therefore, the Cost Price of 3540 articles

And, since the Sale Price of 59 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₉

Therefore, the Sale Price of 3540 articles

= ¹/₅₉ × 3540 = $60

⇒ The Sale Price (SP) of 3540 articles = $60

Now, the Cost Price (CP) of 3540 articles = $59

And, the Sale Price (SP) of 3540 articles = $60

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)

= 60 – 59 = 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}/₅₉

= ¹⁰⁰/₅₉ = 1.69

Thus, profit = 1.69% Answer

Similar Questions

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

(2) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

(3) Bill sold a bicycle for $840. If he purchased it at $600, then calculate his profit and profit percent in this sale.

(4) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(5) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(6) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(7) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(8) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(9) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

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