Question:
By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?
Correct Answer
571.2
Solution And Explanation
Strategy to solve the question
Step (1) Calculate the cost price at given loss percent and the sale price.
Step (2) After gettting the cost price find the sale price at given profit percent.
Solution
Method (1) Formula Method
Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given
Given, the sale price (SP) = $443.7
And, the loss = 13%
Then, the Sale Price (SP) to earn a profit of 12% = ?
Formula to find the cost price when the sale price and loss percent are known
Cost Price (CP) = 100/100 – gain% × SP
Thus, the Cost Price (CP)
= 100/100 – 13 × 443.7
= 100/87 × 443.7
= 100 × 443.7/87
= 44370/87 = 510
Thus, the Cost Price (CP) = $510
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $510
And, profit = 12%
Thus Sale Price (SP) = ?
Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known
Sale Price (SP) = 100 + gain%/100 × Cost Price (CP)
Thus, the Sale Price (SP)
= 100 + 12/100 × 510
= 112/100 × 510
= 112 × 510/100
= 57120/100 = 571.2
Thus, Sale Price (SP) at a profit of 12% = $571.2 Answer
Method (2) Algebraic Method
Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given
Given, the sale price (SP) = $443.7
And, the loss = 13%
Then, the Sale Price (SP) to earn a profit of 12% = ?
Let the Cost Price (CP) = m
Here given loss = 13%
Calculation of loss
loss is calculated on cost price (CP)
Formula to find the loss = loss% of CP
Thus, loss on the cost price of m
= 13% of m
= 13% × m
= 13/100 × m
⇒ loss = 13 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 443.7 = m – 13 m/100
⇒ 443.7 = 100 m – 13 m/100
⇒ 443.7 = 87 m/100
After cross multiplication, we get
443.7 × 100 = 87 m
⇒ 87 m = 443.7 × 100
⇒ m = 443.7 × 100/87
⇒ m = 44370/87 = 510
⇒ m = 510
Thus, the Cost Price (CP) = $510
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 510
And, the profit = 12%
Thus, Sale Price (SP)
= Cost Price (CP) + 12% of Cost Price (CP)
= 510 + 12/100 × 510
= 510 + 12 × 510/100
= 510 + 6120/100
= 510 + 61.2 = 571.2
Thus, Sale Price (SP) at a profit of 12% = $571.2 Answer
Method (3) Unitary Method
Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given
Given, the sale price (SP) = $443.7
And, the loss = 13%
Then, the Sale Price (SP) to earn a profit of 12% = ?
Let, CP = 100
12% profit = 12% of CP
= 12% of 100 = 12
Thus, Sale Price to earn a profit of 12% = CP + 12
= 100 + 12 = 112
⇒ Sale Price to earn a profit of 12% = 112
13% loss = 13% of CP
= 13% of 100 = 13
Thus, Sale Price at a loss of 13% = CP – Loss
= 100 – 13 = 87
⇒ Sale Price at a loss of 13% = 87
∵ If the Sale Price is 87, then to earn a profit of 12% the Sale Price should be = 112
∴ If the Sale Price is 1, then to earn a profit of 12% the Sale Price should be
= 112/87
∴ If the Sale Price is 443.7, then to earn a profit of 12% the Sale Price should be
= 112/87 × 443.7
= 112 × 443.7/87
= 49694.4/87 = 571.2
Thus, Sale Price to get a profit of 12% = $571.2 Answer
Method (4) Shortcut Method
Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given
Given, the sale price (SP) = $443.7
And, the loss = 13%
Then, the Sale Price (SP) to earn a profit of 12% = ?
Here, the Sale Price at a loss of 13 = $443.7
This means 87% of the Cost Price (CP) = 443.7
Therefore, 1% of the Cost Price (CP) = 443.7/87
Therefore, 100% of the Cost Price (CP)
= 443.7/87 × 100 = 510
Thus, the Cost Price (CP) = $510
Now, we need to find the Sale Price at a profit of 12%
Thus, Sale Price at a profit of 12%
= 112% of the Cost Price (CP)
= 112% of 510
= 112/100 × 510 = 571.2
Thus, the Cost Price at a profit of 12% = $571.2 Answer
Similar Questions
(1) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.
(2) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?
(3) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?
(4) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?
(5) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?
(6) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80
(7) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?
(8) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.
(9) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.
(10) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?