Profit And Loss
MCQs Math


Question:     Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5


Correct Answer  10

Solution And Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = 100/100 + gain% × SP

Thus, the Cost Price (CP)

= 100/100 + 5 × 10.5

= 100 × 10.5/105

= 1050/105 = 10

Thus, the Cost Price (CP) = $10 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 5%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 5% of m

= 5% × m

= 5/100 × m

⇒ Profit = 5 m/100

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 10.5 = m + 5 m/100

⇒ 10.5 = 100 m + 5 m/100

⇒ 10.5 = 105 m/100

After cross multiplication, we get

10.5 × 100 = 105 m

⇒ 105 m = 10.5 × 100

⇒ m = 10.5 × 100/105

⇒ m = 1050/105 = 10

⇒ m = 10

Thus, the Cost Price (CP) = $10 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 5% of 100 = 5

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 5

⇒ Sale Price (SP) = 105

∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= 100/105

∴ If the Sale Price (SP) is 10.5, then the Cost Price (CP)

= 100/105 × 10.5

= 100 × 10.5/105

= 1050/105 = 10

Thus, the Cost Price (CP) = $10 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

SP = 105% of CP

⇒ SP = 105/100 × CP

⇒ 10.5 = 105 CP/100

After cross multiplication

⇒ 10.5 × 100 = 105 CP

⇒ 105 CP = 10.5 × 100

⇒ CP = 10.5 × 100/105

⇒ CP = 1050/105 = 10

⇒ CP = $10 Answer


Similar Questions

(1) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(2) Jojo loses 36% by selling an article for $1062.40. For how much should he sell it to get a profit of 35%?

(3) 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.

(4) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

(5) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?

(6) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

(7) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(8) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

(9) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?

(10) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.


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