Question

An item is sold with a profit of \(40\%\). If the cost price is reduced by \(40\%\) and Rs. \(5\) are also reduced from it, then the profit will be increased to \(50\%\). Find the final cost price.

• A. 10
• B. 15
• C. 18
• D. 20

Answer 1

The Correct Option is B

Let the original cost price be $C$.
Step 1: Selling price with 40% profit
\[SP_1 = C + 0.40C = 1.40C\]
Step 2: New cost price and selling price with 50% profit 
The cost price is reduced by 40% and Rs. 5. The new cost price ($C_{\text{new}}$) is:
\[C_{\text{new}} = 0.60C - 5\]
The selling price with a 50% profit is:
\[SP_2 = C_{\text{new}} + 0.50C_{\text{new}} = 1.50C_{\text{new}}\]
Step 3: Equate the selling prices
As the selling price is the same in both scenarios, we can set the two selling prices equal:
\[1.40C = 1.50(0.60C - 5)\]
Step 4: Solve the equation
Distribute on the right side:
\[1.40C = 1.50 \times 0.60C - 1.50 \times 5\]
\[1.40C = 0.90C - 7.5\]
Isolate terms with $C$ on one side:
\[1.40C - 0.90C = -7.5\]
\[0.50C = -7.5\]
Solve for $C$:
\[C = \frac{-7.5}{0.50} = 15\]