Question

By selling an article, Sonu makes a profit of 20%.if the CP decrease by10%and SP also increase by 10%, calculate her profit percentage.

Answer 1

Given

Profit percent₁ = 20%

CP decreases by 10% & SP increases by 10%

To find

Profit percentage₂

Solution

Let the initial CP (CP₁) be Rs.Y.

We know that,

➥ SP = CP + Profit

Putting values :

➝ SP = Y + (Y × 20%)

➝ SP = Y + (Y × 1/5)

➝ SP = Y + Y/5

➝ SP = (5Y + Y)/5

➝ SP₁ = 6Y/5

According to 2nd case :

⟼ SP + 10% of SP = CP - 10% of CP + Profit

⟼ SP + SP/10 = CP - CP/10 + Profit

⟼ (10SP + SP)/10 = (10CP - CP)/10 + Profit

⟼ 11SP/10 = 9CP/10 + Profit

• Putting values of SP & CP

⟼ [11(6Y/5)]/10 = 9Y/10 + Profit

⟼ [66Y/5]/10 = 9Y/10 + Profit

⟼ 66Y/50 = 9Y/10 + Profit

⟼ 33Y/25 = 9Y/10 + Profit

⟼ 33Y/25 - 9Y/10 = Profit

⟼ (66Y - 45Y)/50 = Profit

⟼ 21Y = 50Profit

⟼ Profit = 21Y/50

Now finding Profit%

➻ Profit% = (Profit × 100)/CP

➻ Profit% = (21Y/50 × 100)/Y

➻ Profit% = 21/50 × 100

➻ Profit% = 21 × 2

➻ Profit% = 42%

Therefore,

Her profit percentage = 42% .

Answer 2

$\huge{\underline{\red{\rm{Solution:}}}}$

$\large{\underline{\green{\rm{let:}}}}$

• The cost price of article be X

$\large{\underline{\purple{\rm{Given:}}}}$

• By selling an article, Sonu makes a profit of 20%
• using formula here,

$\sf\green{\longrightarrow SP=\dfrac{100+G\%}{100}*CP}$

$\sf{\implies SP=\dfrac{100+20}{100}*X}$

$\sf{\implies SP=\dfrac{120}{100}*X}$

$\sf\red{\implies SP=\dfrac{6X}{5}}$

$\large{\underline{\purple{\rm{Given:}}}}$

• If the CP decrease by10%and SP also increase by 10%, (here)
• The cost price of article=X
• The selling price of article=6X/5

$\sf{\implies CP=\dfrac{100-10}{100}*X}$

$\sf\red{\implies CP=\dfrac{9X}{10}}$

$\sf{\implies SP=\dfrac{6X}{5}*\dfrac{110}{100}}$

$\sf\red{\implies SP=\dfrac{66X}{50}}$

• Here it's clearly mentioned above that selling price is greater than cost price than we get profit
• using formula here, to p%

$\large{\underline{\purple{\rm{P\%=\frac{SP-CP}{CP}*100:}}}}$

$\sf{\implies P\%=\frac{66X}{50}-\frac{9X}{10}*100/X}$

$\sf{\implies P\%=\frac{21X}{50}*100/X}$

$\sf{\implies P\%=42\%}$