Mastering Profit & Loss Formulas for BCS Math

When solving profit and loss problems in BCS (Bangladesh Civil Service) math, you can use shortcut formulas to save time. Here are some essential formulas and tips:
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Key Terms:

1. Cost Price (CP): The price at which an item is bought.
2. Selling Price (SP): The price at which an item is sold.
3. Profit: When SP CP.
4. Loss: When CP SP.
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Shortcut Formulas:

1. Profit:

Profit = SP - CP

Profit Percentage = (Profit/CP) × 100
2. Loss:

Loss = CP - SP

Loss Percentage = (Loss/CP) × 100
3. Selling Price (SP):

If there’s profit: SP = CP × (1 + Profit%/100)

If there’s loss: SP = CP × (1 - Loss%/100)
4. Cost Price (CP):

If there’s profit: CP = SP / (1 + Profit%/100)

If there’s loss: CP = SP / (1 - Loss%/100)
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Key Tips:

1. For successive profit/loss percentages:
Combined Percentage = (x + y + (xy/100))%,
where x and y are the profit or loss percentages.
2. When a discount is given:
Discount = Marked Price - SP,
Discount Percentage = (Discount/Marked Price) × 100.
3. Direct relationships for fast answers:

If SP is fixed, Profit% ∝ CP (inverse relation).

If CP is fixed, Profit% ∝ SP (direct relation).
Practice applying these formulas to quickly solve profit and loss questions in BCS exams.
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