An article is sold at a profit of 30%. If both cost price and selling

1.	An article is sold at a profit of 30%. If both cost price and selling price of the article are decreased by Rs.100, the profit now would be 45%. The original cost price of the article is:1. Rs. 5002. Rs. 2503. Rs. 3004. Rs. 400
Answer» Correct Answer - Option 3 : Rs. 300 Given: Old profit = 30% New profit = 45% Formula used: \(\;Profit\% \; = \;\frac{{SP\; - \;CP}}{{CP}}\; \times 100\) Calculation: Let the original cost price of the article be X. Old selling price at 30% profit will be = \(\frac{{130}}{{100}}\;x\) ⇒ 1.3x both cost price and selling price of the article are decreased by Rs.100 ∴ New CP = x -100 and new SP = 1.3x - 100 \(\;Profit\% \; = \;\frac{{SP\; - \;CP}}{{CP}}\; \times 100\) \(45\; = \;\frac{{\left( {1.3x\; - \;100} \right)\; - \;\left( {x\; - \;100} \right)}}{{x\; - \;100}}\; \times \;100\;\) ⇒ 0.45x - 45 = 1.3x - 100 - x + 100 ⇒ 0.45x - 0.3x = 45 ⇒ 0.15x = 45 x = 300 c The original cost price is 300

An article is sold at a profit of 30%. If both cost price and selling price of the article are decreased by Rs.100, the profit now would be 45%. The original cost price of the article is:1. Rs. 5002. Rs. 2503. Rs. 3004. Rs. 400

Answer» Correct Answer - Option 3 : Rs. 300

Given:

Old profit = 30%

New profit = 45%

Formula used:

\(\;Profit\% \; = \;\frac{{SP\; - \;CP}}{{CP}}\; \times 100\)

Calculation:

Let the original cost price of the article be X.

Old selling price at 30% profit will be = \(\frac{{130}}{{100}}\;x\)

⇒ 1.3x

both cost price and selling price of the article are decreased by Rs.100

∴ New CP = x -100 and new SP = 1.3x - 100

\(\;Profit\% \; = \;\frac{{SP\; - \;CP}}{{CP}}\; \times 100\)

\(45\; = \;\frac{{\left( {1.3x\; - \;100} \right)\; - \;\left( {x\; - \;100} \right)}}{{x\; - \;100}}\; \times \;100\;\)

⇒ 0.45x - 45 = 1.3x - 100 - x + 100

⇒ 0.45x - 0.3x = 45

⇒ 0.15x = 45

x = 300

c The original cost price is 300

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