Question

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

• A. 10
• B. 20
• C. 14
• D. 15

Answer 1

The Correct Option is C

Let the cost price (CP) of the product be \( x \) rupees. The selling price (SP) is fixed to ensure a 40% profit. Therefore, the SP is:

\[ SP = x + 0.4x = 1.4x \] 

According to the problem, if the cost price were 40% less, it would be:

\[ 0.6x \]

And the selling price would be 5 rupees less, i.e.,

\[ 1.4x - 5 \]

In this scenario, the profit would be 50%, thus:

\[ 1.5 \times 0.6x = 1.4x - 5 \]

\[ 0.9x = 1.4x - 5 \]

Solving the equation:

\[ 1.4x - 0.9x = 5 \]

\[ 0.5x = 5 \]

\[ x = \frac{5}{0.5} = 10 \]

The original selling price is:

\[ SP = 1.4 \times 10 = 14 \]

Thus, the original selling price of the product is 14 rupees.

Answer 2

Let the original cost price be $C$, and the original selling price be $S$. We know that $S = C \times 1.40$. If the cost price is reduced by \(40\%\), the new cost price is $0.6C$, and the new selling price is $S - 5$. The new profit is 50

$S - 5 = 1.5 \times 0.6C \implies S - 5 = 0.9C$

Substitute $S = 1.4C$ into this equation:

\(1.4C - 5 = 0.9C\)
\(\implies 0.5C = 5\)
 \(\implies C = 10\)

The original selling price is $S = 1.4 \times 10 = 14$.