Calculating the Selling Price After Discounts and Loss
Let the Cost Price (CP) of the item be \(C\). The trader marked the price 40% above the cost price. So, the Marked Price (MP) is:
\(MP\) = \(C + (40\% \text{ of } C)\)
\(MP\) = \(C + 0.40C = 1.40C\)
The trader allowed two successive discounts: 20% and 25%. The price after the first discount (20%) is:
\(Price after 1st discount\) = \(MP \times (1 - 0.20)\)
\(Price after 1st discount\) = \(MP \times 0.80\)
The final Selling Price (SP) after the second discount (25%) is:
\(SP\) = (\(Price after 1st discount\)) \(\times (1 - 0.25)\)
\(SP\) = (\(MP \times 0.80\)) \(\times 0.75\)
\(SP\) = \(MP \times (0.80 \times 0.75)\)
\(SP\) = \(MP \times 0.60\)
Now, substitute the expression for MP in terms of C:
\(SP\) = \((1.40C) \times 0.60\)
\(SP\) = \(0.84C\)
The trader incurred a loss of ₹224. The formula for loss is:
\(Loss\) = \(CP - SP\)
Given Loss = ₹224:
\(224 = C - 0.84C\)
\(224 = 0.16C\)
Solve for the Cost Price (C):
\(C = \frac{224}{0.16}\)
\(C = 1400\)
So, the Cost Price is ₹1400.
Determining the Final Selling Price
Now, calculate the Selling Price (SP) using the calculated Cost Price:
\(SP\) = \(0.84C\)
\(SP\) = \(0.84 \times 1400\)
\(SP\) = \(1176\)
The selling price of the item is ₹1,176.
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