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

Answer: (B)

15

Answer 2

Let the original cost price be $C$.
Step 1: Selling price when the profit is 40%
$SP_1 = C + 0.40C = 1.40C$
Step 2: New cost price and selling price when the profit is 50%
The new cost price is reduced by 40% and Rs. 5. Therefore, the new cost price ($C_{\text{new}}$) is:
$C_{\text{new}} = 0.60C - 5$
The selling price when the profit is 50% is:
$SP_2 = C_{\text{new}} + 0.50C_{\text{new}} = 1.50C_{\text{new}}$
Step 3: Equating the selling prices
Since the selling price remains the same for both situations, we can equate the two selling prices:
$1.40C = 1.50(0.60C - 5)$
Step 4: Solve the equation
Expand both sides:
$1.40C = 1.50 \times 0.60C - 1.50 \times 5$
$1.40C = 0.90C - 7.5$
Move all terms involving $C$ to one side:
$1.40C - 0.90C = -7.5$
$0.50C = -7.5$
Solving for $C$:
$C = \frac{-7.5}{0.50} = 15$