Question

An article is sold at a profit of 20%. If the cost price is increased by 10% and the sale price by Rs.26, then the percentage of profit reduces by 5%. Determine the cost price.

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Answer 1

$\Large\red\bigstar{\text{\underline{\underline{\: Question:-}}}}$

An article is sold at a profit of 20%. If the cost price is increased by 10% and the sale price by Rs.26, then the percentage of profit reduces by 5%. Determine the cost price.

$\Large\red\bigstar{\text{\underline{\underline{\: Solution:-}}}}$

• Let the CP of the article be x

• Profit percent = 20%

then,

⇒ $\large{\sf{SP=\frac{100+Profit\:percent}{100}×CP}}$

⇒$\large{\sf{SP=\frac{100+20}{100}x}}$

∴$\large{\sf{SP=\frac{6x}{5}}}$

According to the Question :-

• CP is increased by 10%

⇒ CP (new) = (10% of x) + x

⇒ CP (new) = $\large{\sf{\frac{10x}{100}+x}}$

∴ CP (new) = $\large{\sf{\frac{11x}{10}}}$

• SP is increased by 26 Rs.

⇒ SP (new) = $\large{\sf{\frac{6x}{5}+26}}$

∴ SP (new) = $\large{\sf{\frac{6x+130}{5}}}$

• Profit percent is reduced by 5%

⇒ Profit % (new) = 20% - 5%

∴ Profit % (new) = 15%

Therefore,

⇒Profit (new) = SP - CP

⇒ Profit (new) = $\large{\sf{\frac{6x+130}{5}-\frac{11x}{10}}}$

⇒Profit (new) = $\large{\sf{\frac{260+x}{10}}}$

∴ Profit (new) = $\large{\sf{\frac{260+x}{10}}}$

Now, By equating :-

⇒ $\large{\sf{Profit\: percent=\frac{Profit}{CP}×100}}$

⇒$\large{\sf{15=\frac{260+x}{10}×\frac{10}{11x}×100}}$

⇒$\large{\sf{15=\frac{260+x}{11x}×100}}$

⇒$\large{\sf{\frac{3}{20}=\frac{260+x}{11x}}}$

• Cross multiplication :-

⇒$\large{\sf{33x=20(260+x)}}$

⇒$\large{\sf{33x=5200+20x}}$

⇒$\large{\sf{33x-20x=5200}}$

⇒$\large{\sf{13x=5200}}$

⇒$\large{\sf{x=\frac{5200}{13}}}$

∴ x = 400

$\Large\red\bigstar{\text{\underline{\underline{\: Answer}}}}$

Therefore, the cost price of the article was ₹400

Answer 2

• The cost price of the article is equal to Rs. 400.

Given :-

• An article is sold at a profit of 20%.
• When cost price is increased by 10% and the sale price by Rs.26, then the percentage of profit reduces by 5% .

To Find :-

• The cost price of the article ?

Formula used :-

• Selling price (SP) = {Cost price × (100 + Profit %)}/100
• Profit = SP - CP
• Profit % = (Profit × 100) / CP

Solution :-

Let us assume that, the cost price (CP) of the article is equal to Rs. 100x .

Case 1) :-

→ CP of article = Rs. 100x

→ Profit = 20%

→ SP of article = {CP × (100 + Profit%)}/100 = {100x × (100 + 20)}/100 = (100x × 120)/100 = Rs. 120x ----- Equation (1)

Case 2) :-

→ CP of article = Rs. 100x

→ CP increased by = 10%

So,

→ New CP = 100x + 10% of 100x

→ New CP = 110% of 100x

→ New CP = (110 × 100x)/100

→ New CP = Rs. 110x ------- Equation (2)

and,

→ New SP = Equation (1) + Rs. 26

→ New SP = Rs.(120x + 26) ------- Equation (3)

also,

→ Profit reduced by = 5%

So,

→ New profit = 20% - 5% = 15% ------ Equation (4)

from Equation (2) and Equation (3) we get,

→ New Profit = New SP - New CP

→ New Profit = (120x + 26) - 110x

→ New Profit = 120x - 110x + 26

→ New Profit = Rs.(10x + 26)

comparing new profit % with Equation (4) now,

→ (Profit × 100) / CP = New profit

→ {(10x + 26) × 100)} / 110x = 15

→ 100(10x + 26) = 110x × 15

dividing both sides by 10,

→ 10(10x + 26) = 11x × 15

→ 100x + 260 = 165x

→ 165x - 100x = 260

→ 65x = 260

→ 65x = 4 × 65

dividing both sides by 65,

→ x = 4

therefore, putting value of x we get,

→ The cost price of the article = Rs. 100x

→ The cost price of the article = 100 × 4

→ The cost price of the article = Rs. 400

Hence, the cost price of the article is equal to Rs. 400 .

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