A shopkeeper who incurred a loss in a certain deal, finds that the difference between the selling and cost price is 16(2/3)% of their sum. By what percentage should the selling price have been increased, so that it would have been a break-even deal?
Answers
Step-by-step explanation:
Let take cost price = x ,
then by formula
S.P = ((100 - L%)/100)* C.P
S.P = (80/100)* x = (4/5) x
Now if he sell 200 more,
S.P = (4/5)x + 200
Profit will 5 %
S.P = ((100 + P% )/100) * C.P
=> (4/5)x + 200 = ((100 + 5)/100) * x
25x = 20000
x = 800
C.P is ₹ 800
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Therefore the percentage increase in selling price to make it a break-even deal is 40%.
Given:
The difference between the selling price and cost price is 16 (2/3)% of their sum when the loss is incurred by the shopkeeper.
To Find:
To make it a break-even deal, for what percentage should be increased?
Solution:
The given question can be solved very easily as shown below.
Let the selling price of the product during the loss be SP.
Let the cost price of the product be CP.
Given that,
⇒ CP - SP = 16.67% ( CP + SP )
⇒ CP - SP = 0.167 ( CP + SP )
⇒ CP - 0.167CP = 0.167SP + SP
⇒ 0.833CP = 1.167SP
⇒ SP = 0.714CP____(i.)
If the break-even deal is made, the selling price must equal the cost price.
⇒ SP₁ = CP____(ii.)
The increase in the percentage of the Selling price is calculated as shown below,
⇒ Percentage increase in SP = [ ( SP₁ - SP ) / SP ] × 100
⇒ Percentage increase in SP = [ ( CP - 0.714CP ) / 0.714CP ] × 100
⇒ Percentage increase in SP = [ ( 1 - 0.714 ) / 0.714 ] × 100
⇒ Percentage increase in SP = ( 0.286/0.714 ) × 100 = 0.4 × 100 = 40%
Therefore the percentage increase in selling price to make it a break-even deal is 40%.
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