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