Profit Loss Master - Quick Revision
Profit Loss Master – Quick Revision
One-Liners
- CP = Cost at which article is bought.
- SP = Price at which article is sold.
- Profit = SP – CP (only when SP > CP).
- Loss = CP – SP (only when CP > SP).
- Profit % = (Profit / CP) × 100.
- Loss % = (Loss / CP) × 100.
- Discount is always calculated on Marked Price (MP).
- If two articles sold at same price, one at p% profit & other at p% loss, net loss = (p² / 100) %.
- When CP of x = SP of y, Profit % = [(x – y)/y] × 100.
- If profit is p%, SP = CP × (100 + p)/100.
- If loss is l%, SP = CP × (100 – l)/100.
- To get x% profit on SP, CP = SP × 100 / (100 + x).
- Successive discounts a% & b% give equivalent discount = [a + b – (ab/100)] %.
- False weight: Gain % = (Excess / True weight) × 100.
- Article sold at 1/n of CP ⇒ Loss % = [1 – 1/n] × 100.
- Article sold at 2 times CP ⇒ Profit % = 100 %.
- Mark-up above CP x%, then max discount d% allowed without loss: d ≤ [100x/(100 + x)] %.
- Overall profit/loss on two transactions = combine absolute profits/losses, never average percentages.
- Always take CP as 100 % base to avoid fraction errors.
- Break-even ⇒ SP = CP ⇒ Zero profit, zero loss.
Formulas / Rules
| Formula | Use |
|---|---|
| Profit % = (SP – CP)/CP × 100 | Convert profit to percentage |
| Loss % = (CP – SP)/CP × 100 | Convert loss to percentage |
| SP = CP × (100 ± g)/100 | Find selling price for gain/loss g% |
| CP = SP × 100 / (100 ± g) | Find cost price given SP & g% |
| Equivalent Discount = d₁ + d₂ – d₁d₂/100 | Combine two successive discounts |
| Marked Price = CP × (100 + m)/100 | When mark-up m% is on CP |
| Gain by false weight = (Excess / True) × 100 | Dealer gives less weight |
| Net effect of equal % profit & loss on same CP = (p²/100)% loss | Two separate sales, same CP |
| Overall Profit/Loss % = (Total Profit or Loss / Total CP) × 100 | Multiple items, one transaction |
| If x goods bought for 1 rupee & sold y goods for 1 rupee, Profit % = [(x – y)/y] × 100 | Special rate-based profit |
Memory Tricks
- SPicy Formula: SP = CP × (100 ± P%) → “Spice it up for profit, spice it down for loss.”
- Discount Dance: Equivalent discount always “add then subtract product-over-hundred.”
- Same-Price-Same-Percent: Same CP, same % gain & loss → remember “square-the-percent-loss”.
- False Weight Fear: Gain% = (cheated / true) × 100 → “Cheated on weight, cheated on profit.”
- CP-is-King: Every percentage is calculated ON CP – say “C-for-Centre, C-for-CP.”
Common Errors
| Error | Correct |
|---|---|
| Taking SP as base for profit % | Always use CP as base |
| Adding discounts directly (20% + 10% = 30%) | Use formula d₁+d₂–d₁d₂/100 = 28% |
| Averaging profit & loss % for net effect | Compute absolute profit/loss first, then % on total CP |
| Using MP instead of CP for profit % | Profit is on CP, discount is on MP |
| Forgetting to convert % to decimal in SP/CP formulas | Divide percentage by 100 before substitution |
5 Quick MCQs
Question 1
A trader marks his goods 40 % above CP and gives a discount of 20 %. What is the profit %?A) 12 % B) 15 % C) 20 % D) 8 %
Answer
A) 12 %Question 2
By selling 8 pens a man gains cost price of 2 pens. His gain % isA) 20 % B) 25 % C) 30 % D) 15 %
Answer
B) 25 %Question 3
A machine is sold at a loss of 10 %. Had it been sold for ₹ 90 more, there would have been a gain of 5 %. The CP isA) ₹ 500 B) ₹ 600 C) ₹ 800 D) ₹ 900
Answer
B) ₹ 600Question 4
Two articles are sold at ₹ 1,000 each, one at 25 % profit and the other at 25 % loss. Net result isA) No loss no gain B) 6.25 % loss C) 6.25 % gain D) 5 % loss
Answer
B) 6.25 % lossQuestion 5
A dealer uses 900 g instead of 1 kg. His gain % isA) 10 % B) 11.11 % C) 12.5 % D) 9.09 %
BETA
