Profit, Loss & Discount

The most practical chapter. Master the 'Ratio Method' for Profit%, the 'MP-CP Relation' for Discounts, and the 'Dishonest Dealer' concepts.

1. The Golden Ratio (CP:SP)

Avoid formulas like $SP = CP(100+P)/100$ . Use Ratios.

20% Profit: $1/5 \to CP=5, SP=6$ .
20% Loss: $1/5 \to CP=5, SP=4$ .
Profit on SP: If 20% on SP, $1/5 \to SP=5, Profit=1 \implies CP=4$ . Actual P% = $1/4 = 25\%$ .

Example:

Q: Profit is 25% of Selling Price. Find actual Profit %.

Solution:

25\% = 1/4 (P/SP)

. SP=4, P=1

\to

CP=3.
Actual % =

1/3 = 33.33\%

Direct relation between CP, MP, Profit%, and Discount%.

Example:

Q: Discount 10%, Profit 20%. If CP=900, find MP.

Solution:

CP/MP = (100-10)/(100+20) = 90/120 = 3/4

3 \to 900

MP = 4 \to 1200

Profit comes from using less weight.

Formula: $\frac{\text{True Weight}}{\text{False Weight}} = \frac{100+P\%}{100\pm x\%}$ .
Logic: If he uses 900g for 1kg, he sells 900g but charges for 1000g. Profit = 100g on 900g CP.

Example:

Q: Uses 800g instead of 1kg. Sells at CP. Find Profit %.

Solution: Error = 200g. Base (False Weight) = 800g.

P\% = (200/800) \times 100 = 25\%

Effective Discount calculation.

Rule: Free items are the Discount. Total items (Paid + Free) are the MP base.
$\text{Discount \%} = \frac{\text{Free}}{\text{Total}} \times 100$ .

Example:

Q: Buy 3 Get 2 Free. Discount %?

Solution: Free=2. Total=5.

D\% = (2/5) \times 100 = 40\%

Net price after multiple discounts.

Formula: $x + y - xy/100$ (Note the signs: $-D_1 - D_2 + D_1D_2/100$ ).
Ratio: If 10% and 10% off: $10 \to 9, 10 \to 9 \implies 100 \to 81$ . Net 19% off.

Example:

Q: Two successive discounts of 20% and 10%.

Solution: Ratio:

5 \to 4

and

10 \to 9

50 \to 36

. Drop 14.

14/50 = 28\%

. Or

-20 -10 + 2 = -28\%

Common Scenario: Two items sold at same Price.

Example:

Q: Sold two cars at 1 Lakh each. One 20% profit, other 20% loss.

Solution: Same SP. Loss =

20^2/100 = 4\%