Profit & Loss – MBA CUET PG – Notes & Practice Questions

Basic Terms

• Cost Price (CP): Price at which an article is bought.

• Selling Price (SP): Price at which an article is sold.

• Profit / Gain: $\text{SP} – \text{CP}$

• Loss: $\text{CP} – \text{SP}$

Fundamental Formulas

Profit / Loss:

$$\text{Profit} = SP – CP$$
$$\text{Loss}=CP-SP$$

Profit% & Loss%:

$$\text{Profit\%} = \frac{\text{Profit}}{CP} \times 100$$
$$\text{Loss\%}=\frac{\text{Loss}}{CP}\times 100$$

SP & CP Formulas:

$$SP = CP \times \left(1 + \frac{P\%}{100}\right)$$
$$SP = CP \times \left(1 – \frac{L\%}{100}\right)$$
$$CP = \frac{SP}{1 + \frac{P\%}{100}}$$ $$CP = \frac{SP}{1 – \frac{L\%}{100}}$$

Marked Price (MP) & Discount

$$\text{Discount} = MP – SP$$
$$\text{Discount\%} = \frac{MP – SP}{MP} \times 100$$

$$SP = MP(1 – \frac{D}{100})$$

If successive discounts:
For discounts $\mathrm{a\% }\mathrm{<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;">and </span>}$$b\%$

$$\text{Net Discount} = a + b – \frac{ab}{100}$$

Profit on Selling Price vs. Cost Price

If profit is x% on SP,

$$\text{Profit\% on CP} = \frac{x}{100-x} \times 100$$

If profit is x% on CP,

$$\text{Profit\% on SP} = \frac{x}{100+x} \times 100$$

Short Tricks & Rapid Conversions

SP/CP ratio shortcut:

If profit = $\mathrm{P\%}\mathrm{}$

$$SP : CP = (100 + P) : 100$$

If loss = L%

$$SP : CP = (100 – L) : 100$$

Discount then Profit Scenario:

If

• Cost price → CP

• Marked price carries profit p%

• Discount given = d%

Then final profit%:

$$\text{Final Profit\%} = p – d + \frac{pd}{100}$$

Successive Profit/Loss Trick:

Profit % = a%, then again b%:

$$\text{Net Gain\%} = a + b + \frac{ab}{100}$$

Loss % = a%, b%:

$$\text{Net Loss\%} = a + b – \frac{ab}{100}$$

Profit a% then loss b%:

$$\text{Net Result\%} = a – b – \frac{ab}{100}$$

Cost Price Adjustments

When CP is increased or decreased:

If CP changes by x% and SP unchanged:

• Increase in CP (x%):

$$\text{Profit\% reduces by } x\% + \frac{x \cdot \text{Old Profit\%}}{100}$$

• Decrease in CP (x%):

$$\text{Profit\% increases by } x\% + \frac{x \cdot \text{Old Profit\%}}{100}$$

Quantity-Based Profits

Selling one article at profit equal to CP of another

If: Profit on one item = CP of another identical item
→ Profit% = 100%

Buy n items, get 1 free

Effective discount:

$$\text{Discount} = \frac{1}{n+1} \times 100\%$$

Shopkeeper Tricks

False Weight

If a shopkeeper uses (x% less weight) but sells at CP:

$$\text{Gain\%} = \frac{x}{100-x} \times 100$$

Mixing two items

If two items of CPs \(C_1\) and \(C_2\)​ are mixed in ratio w1:w2${}_{}$

Average CP:

$$\text{CP}_{avg} = \frac{w_1C_1 + w_2C_2}{w_1 + w_2}$$​​

Important Practical Shorts

• 25% profit → multiply CP by 1.25

• 20% loss → multiply CP by 0.8

• 12.5% = $\frac{1}{8}$

• 16⅔% = $\frac{1}{6}$

• 33⅓% = $\frac{1}{3}$

• 50% = $\frac{1}{2}$

More Tricks

To double the money → 100% profit

If SP is x% more than CP

Profit% = x%

If SP is x% of CP

Profit% = x% – 100

If CP is x% of SP

Loss% = 100 – x%

Two items trick

If two articles are sold at the same SP, one at x% profit and other at x% loss →
Overall result is always a loss:

$$\text{Loss\%} = \frac{x^2}{100}$$

Practice Questions​

1. A shopkeeper marks an item 40% above CP and gives a discount of 25%. Find the profit%.
A) 5%
B) 10%
C) 12.5%
D) 15%

2. A man sells an article at 20% profit. Had he sold it for ₹60 more, his profit would have been 30%. Find CP.
A) 400
B) 500
C) 600
D) 300

3. An article is sold at 25% loss. Had it been sold for ₹150 more, there would have been 20% profit. Find CP.
A) 250
B) 300
C) 350
D) 400

4. If SP is 80% of MP and CP is 70% of MP, find profit%.
A) 10%
B) 12%
C) 14.28%
D) 8%

5. A shopkeeper sells two articles at same SP. On one he gains 20%, on other he loses 20%. Find overall result.
A) 4% loss
B) 4% profit
C) 2% loss
D) 2% profit