Percentages, Profit and Loss
Overview
Percentages, Profit and Loss is one of the highest-scoring topics in Railway NTPC and Group D exams. Every year 2-4 questions appear from this chapter. Core ideas include converting fractions to percentages, calculating profit/loss on cost price, discount on marked price, and successive percentage changes. Mastering a few key formulas and fraction-to-percentage shortcuts can save crucial minutes in the exam hall.
Typed Notes
Percentage Basics and Conversion
Percent means 'per hundred'. To convert a fraction to percent, multiply by 100. Example: 3/4 = 75%. To convert percent to fraction, divide by 100. Example: 35% = 35/100 = 7/20. Percentage increase = (Increase / Original) × 100. Percentage decrease = (Decrease / Original) × 100. Exam Tip: If a value increases by x% then decreases by x%, the net result is always a LOSS of (x²/100)%. Example: 10% up then 10% down = net loss of 1%. This trick appears repeatedly in NTPC papers.
Profit and Loss — Core Formulas
Cost Price (CP) = price at which goods are bought. Selling Price (SP) = price at which goods are sold. If SP > CP → Profit = SP − CP. If SP < CP → Loss = CP − SP. Profit% = (Profit/CP) × 100. Loss% = (Loss/CP) × 100. To find CP when SP and Profit% are known: CP = SP × 100 / (100 + Profit%). To find CP when SP and Loss% are known: CP = SP × 100 / (100 − Loss%). Memory Hook: 'CP is the BASE — profit and loss percentages always sit on CP.'
Marked Price, Discount and Dishonest Traders
Marked Price (MP) is the printed/listed price. Discount reduces MP to get SP. SP = MP × (100 − d%) / 100. A trader marks goods x% above CP and gives y% discount: Net Profit% = x − y − (xy/100). Dishonest trader trick: A shopkeeper uses a false weight of W grams instead of 1000 g and claims to sell at CP. Profit% = (1000 − W) / W × 100. Example: Uses 900 g weight → Profit% = 100/900 × 100 = 11.11%. This exact type appears in Group D papers frequently.
Successive Changes and Equivalent Discount
When two successive discounts a% and b% are given, the single equivalent discount = (a + b − ab/100)%. Example: 20% and 10% successive discounts → equivalent = 20 + 10 − (20×10/100) = 30 − 2 = 28%. Similarly, if price increases by a% then by b%, net change = (a + b + ab/100)%. For three successive changes, apply the formula twice. Exam Tip: In NTPC, questions often give two discounts and ask for equivalent discount or final SP — use this formula directly to save 2 minutes per question.
Key Concepts
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- 01Profit % = (Profit / Cost Price) × 100; Loss % = (Loss / Cost Price) × 100 — always calculated on Cost Price (CP), never on Selling Price.
- 02SP = CP × (100 + Profit%) / 100 for profit; SP = CP × (100 − Loss%) / 100 for loss — these two formulas cover 80% of exam questions.
- 03Marked Price (MP) and Discount: SP = MP × (100 − Discount%) / 100; Discount is always calculated on Marked Price.
- 04Successive discounts of a% and b%: Equivalent single discount = (a + b − ab/100)% — a favourite formula in NTPC papers.
- 05Key fraction-to-percent shortcuts: 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 ≈ 14.28%, 1/8 = 12.5%, 1/3 = 33.33% — memorise these to solve questions in under 30 seconds.
Questions & Solutions
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A shopkeeper buys an article for ₹800 and sells it for ₹1000. Find the profit percentage.
If an article is sold at ₹540 at a loss of 10%, find the Cost Price.
A trader marks his goods 40% above cost price and gives a discount of 20%. Find his profit or loss percentage.
Two successive discounts of 30% and 20% are offered on an article. Find the equivalent single discount.
A dishonest shopkeeper uses a weight of 800 g instead of 1 kg (1000 g) and sells goods at the cost price. What is his profit percentage?
Profit and Loss questions in Railway exams test CP-SP relationships, discount on marked price, and successive percentage changes. Always remember: profit/loss % is on CP; discount % is on MP. Key shortcuts — successive discount formula, false-weight profit formula, and fraction-to-percent table — can help you solve 3-mark questions in under 45 seconds. Practice 10 questions daily for exam readiness.
Chapter-end quiz
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Q1.An item is bought for ₹500 and sold for ₹450. What is the loss percentage?
Q2.A price is increased by 20% and then decreased by 20%. The net effect on the original price is:
Q3.Marked price of an article is ₹1200. A discount of 15% is given. Find the Selling Price.
Q4.If SP = ₹660 and Profit% = 10%, what is the Cost Price?
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