Profit & Loss – Quick Study Notes
(NABARD Grade‑A Quantitative Aptitude – Quantitative Aptitude Section)
1. Simple Explanation
| Term | Symbol | Meaning | Formula |
|---|---|---|---|
| Cost Price | CP | Price paid to acquire an item | – |
| Selling Price | SP | Price at which item is sold | – |
| Profit | P | Amount by which SP exceeds CP | (P = SP - CP) |
| Loss | L | Amount by which CP exceeds SP | (L = CP - SP) |
| Profit/Loss % | %P/%L | Ratio of profit/loss to CP, expressed in percent | (\displaystyle %P = \frac{P}{CP}\times100) (\displaystyle %L = \frac{L}{CP}\times100) |
Key idea – All profit/loss problems are built on the basic relation (SP = CP \pm) profit/loss.
2. Key Points & Formulas
| Topic | Formula(s) | Notes |
|---|---|---|
| Single item | (SP = CP + P) (SP = CP - L) |
Use %P or %L to express P or L |
| Profit / Loss % | (\displaystyle %P = \frac{SP-CP}{CP}\times100) (\displaystyle %L = \frac{CP-SP}{CP}\times100) |
If given %P, (SP = CP\left(1+\frac{%P}{100}\right)) |
| Multiple items (different quantities) | Total CP = (\sum CP_i) Total SP = (\sum SP_i) Overall %P = (\frac{Total\ SP - Total\ CP}{Total\ CP}\times100) |
Treat each item as a separate transaction; sum the CP and SP |
| Rate of profit for mixed purchases | Suppose you buy (n_1) units at CP₁ and (n_2) units at CP₂, then sell all at the same SP. (\displaystyle %P = \frac{SP - \frac{n_1 CP_1 + n_2 CP_2}{n_1+n_2}}{ \frac{n_1 CP_1 + n_2 CP_2}{n_1+n_2}}\times100) |
Equivalent to “average cost price” method. |
| Mark‑up & Mark‑down | Mark‑up = (\frac{SP-CP}{CP}\times100) Mark‑down = (\frac{CP-SP}{CP}\times100) |
Same as profit % and loss % respectively. |
| Profit/Loss with discount | (SP_{after\ discount} = SP_{original}\left(1 - \frac{discount%}{100}\right)) | Combine with profit % if needed. |
| Profit on a sale after return | (\text{Net SP} = SP_{\text{gross}} - \text{returned amount}) | Adjust CP accordingly if return is at cost price. |
| Ratio of CP to SP | (\frac{CP}{SP} = \frac{100}{100 \pm %P}) | Useful for quick back‑calculations. |
3. Worked Example
Problem
A trader bought items in two lots:
- 150 units of Item A at ₹50 each.
- 200 units of Item B at ₹30 each.
He sold all the items at:
- Item A at ₹60 each.
- Item B at ₹40 each.
Find the overall profit percent.
Step‑by‑Step Solution
| Item | Quantity | CP per unit | Total CP | SP per unit | Total SP |
|---|---|---|---|---|---|
| A | 150 | ₹50 | (150 \times 50 = ₹7{,}500) | ₹60 | (150 \times 60 = ₹9{,}000) |
| B | 200 | ₹30 | (200 \times 30 = ₹6{,}000) | ₹40 | (200 \times 40 = ₹8{,}000) |
Total
- Total CP = ₹7,500 + ₹6,000 = ₹13,500
- Total SP = ₹9,000 + ₹8,000 = ₹17,000
Profit
(