Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

Correct Answer  2.04%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 50 articles = $1

The Sale Price (SP) for 49 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 50 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₀

∵ The Sale Price (SP) for 49 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₉

Calculation of profit

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

= ¹/₄₉ – ¹/₅₀

= ^{50 – 49}/₂₄₅₀

⇒ Profit = ¹/₂₄₅₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₀, the the profit = ¹/₂₄₅₀

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

= ^{1/₂₄₅₀}/_¹/50

= ¹/₂₄₅₀ × ⁵⁰/₁

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

= ¹/₂₄₅₀ × ⁵⁰/₁ × 100

= ^{1 × 50 × 100}/_{2450 × 1}

= ⁵⁰⁰⁰/₂₄₅₀ = 2.04

Thus, Profit = 2.04% 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 50 articles = $1

And, the Sale Price (SP) of 49 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 50 and 49 = 2450

Now, Let total number of articles purchased = 2450

Here, since the Cost Price of 50 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₀

Therefore, the Cost Price of 2450 articles

And, since the Sale Price of 49 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₉

Therefore, the Sale Price of 2450 articles

= ¹/₄₉ × 2450 = $50

⇒ The Sale Price (SP) of 2450 articles = $50

Now, the Cost Price (CP) of 2450 articles = $49

And, the Sale Price (SP) of 2450 articles = $50

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)

= 50 – 49 = 0.99999999999999

⇒ Profit = $0.99999999999999

Calculation of Profit percent using the formula

Formula to calculate the profit percent

Profit percent = ^{Profit × 100}/_{Cost Price}

Thus, profit % = ^{0.99999999999999 × 100}/₄₉

= ^{99.999999999999}/₄₉ = 2.04

Thus, profit = 2.04% Answer

Similar Questions

(1) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?

(2) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(3) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

(4) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(5) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

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

(7) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(8) Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50

(9) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

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