Profit & loss

Profit & Loss – Quick Study Notes

(Suitable for USMLE Quantitative Aptitude)

1. Simple Explanation

• Cost Price (CP) – What you paid to acquire an item.
• Selling Price (SP) – What you charge the customer.
• Profit – SP – CP (positive when SP > CP).
• Loss – CP – SP (positive when CP > SP).

Profit or loss is always expressed as a percentage of the Cost Price.

2. Key Points

3. Worked Example

Problem
A pharmacist buys 30 packs of a medication at $8 each.
He sells them at a 15 % profit on the cost price.
What is the selling price per pack and the total profit?

Solution

1. Cost Price per pack
   [ CP = $8 ]

2. Profit %
   [ \text{Profit%} = 15% ]

3. Selling Price per pack
   [ SP = CP \times \left(1 + \frac{15}{100}\right) = 8 \times 1.15 = $9.20 ]

4. Total Cost (for 30 packs)
   [ 30 \times 8 = $240 ]

5. Total Selling Price
   [ 30 \times 9.20 = $276 ]

6. Total Profit
   [ \text{Profit} = 276 - 240 = $36 ]

7. Profit % (verification)
   [ \frac{36}{240} \times 100 = 15% ]

Answer

• Selling price per pack: $9.20
• Total profit: $36 (15 % on cost)

4. Quick Revision Summary

• Profit = SP – CP
• Loss = CP – SP
• Profit % = (Profit / CP) × 100
• Loss % = (Loss / CP) × 100
• SP from CP & %
  • Profit: SP = CP × (1 + %/100)
  • Loss: SP = CP × (1 – %/100)
• CP from SP & %
  • Profit: CP = SP ÷ (1 + %/100)
  • Loss: CP = SP ÷ (1 – %/100)
• Break‑even: SP = CP → 0 % profit/loss
• Quick mental tip: multiply the CP by the decimal equivalent of the percent (e.g., 20 % = 0.20) to find the profit amount.

Use these formulas in a step‑by‑step fashion:

1. Identify known values (CP, SP, percent).
2. Decide whether a profit or loss is involved.
3. Apply the appropriate formula