SATHEE: Profit Loss Quick Methods

Profit Loss Quick Methods - Quick Revision

CP → Cost Price, SP → Selling Price, MP → Marked Price
Profit = SP – CP; Loss = CP – SP
Profit % = (Profit/CP) × 100; Loss % = (Loss/CP) × 100
If SP = CP, Profit/Loss = 0
100% profit means SP = 2 × CP
50% loss means SP = 0.5 × CP
Discount = MP – SP; Discount % = (Discount/MP) × 100
If two articles sold at same price, one at x% profit & other at x% loss → overall loss = (x²/100)%
To gain x% after giving y% discount on MP → MP = CP × (100+x)/(100–y)
Equal % profit & % loss on same CP → net loss = (Common%)²/100
False weight: Gain % = (Error/True Wt) × 100
Successive discounts a% & b% → single discount = a+b–ab/100
When profit % & loss % are equal, net effect is always LOSS
Mark-up above CP by m% and discount d% given → net profit = m–d–md/100
CP of 1 article = Total CP / Total articles (never use SP here)

Formula/Rule	Application
SP = CP × (100 ± P/L%) / 100	Convert any CP/SP with given %
CP = SP × 100 / (100 ± P/L%)	Reverse calculation
MP = CP × (100 + G%) / (100 – D%)	Marked price to ensure desired gain after discount
Overall Gain/Loss % = (Total Gain/Loss ÷ Total CP) × 100	Multi-item transactions
Single equivalent discount = a + b – ab/100	Two successive discounts
False weight gain % = (Excess / True weight) × 100	Cheating scale problems
When 2 items sold at same SP with x% profit & x% loss → Net loss = x²/100 %	Shortcut for ‘two articles’ trap
If profit & loss both = x% on same CP → Net loss = x²/100 %	Common equality case
Net profit after m% mark-up & d% discount = m – d – md/100	Combined mark-up & discount
CP per article = Total CP ÷ Quantity	Always base % on this CP

Mistake	Correct Approach
Taking SP as base for Profit %	Always use CP in denominator
Adding discounts (20% + 10% = 30%)	Use formula a+b–ab/100 = 28%
Forgetting to convert % to decimal	Divide by 100 before substitution
Using MP instead of CP in profit calc	Compute CP first, then apply profit %
Ignoring weight error unit	Keep both weights in same unit (g, kg) before ratio

1. A man gains 20% by selling an article for ₹480. What is the CP?

₹400 (Solution: CP = 480×100/120 = 400)

2. Two pens sold at ₹10 each, one at 25% profit, other at 25% loss. Net effect?

4% loss (x²/100 = 25²/100 = 6.25 → wait! 25²/100 = 6.25% loss on whole; but per pen CP differ, overall loss = 4%)

3. After giving 10% discount, a shopkeeper still gains 17%. How much % above CP was MP?

30% (MP/CP = (100+17)/(100–10) = 117/90 = 1.3 → 30% above)

4. Successive discounts of 20% and 10% are equal to a single discount of

28% (20+10–20×10/100 = 28%)

5. A dealer uses 900 g instead of 1 kg. His gain % is

11 1/9 % (100/900 ×100 = 11.11%)