Profit and Loss Questions for RRB NTPC

Core Definitions

Cost Price (CP) is what you pay to buy or produce an item. Selling Price (SP) is what you sell it for. If SP is more than CP, you earn a Profit. If SP is less than CP, you suffer a Loss. Marked Price (MP) or List Price is the price written on the tag before any discount is applied.

• Profit = SP - CP (when SP > CP)
• Loss = CP - SP (when CP > SP)
• Profit% and Loss% are always calculated on CP, not SP
• Discount is always calculated on MP, not CP
• SP after discount = MP x (1 - Discount%/100)

Marked Price and Discount

In real-world selling, shopkeepers first mark up the price (MP), then offer a discount. The actual SP is after the discount. RRB NTPC frequently asks you to find either the MP or the actual profit when both markup and discount are given together.

• Discount% is always on MP
• SP = MP x (100 - Discount%) / 100
• Markup% is on CP: MP = CP x (100 + Markup%) / 100
• Even after discount, a profit can exist if markup > discount
• Net result formula: Profit% = [(100 + Markup%) x (100 - Discount%) / 100] - 100

Successive Discounts

When two discounts are given one after another (like 20% then 10%), they are NOT simply added. The second discount applies to the already-reduced price. RRB NTPC has repeatedly tested this concept in tricky wording.

• Two discounts a% and b% together equal: a + b - (ab/100) percent
• Never add two discount percentages directly
• Successive discounts can also apply to markup: treat like chain percentages
• Formula works for any two successive percent changes

Dishonest Dealer and Faulty Weights

A very common RRB NTPC trap question: a dealer claims to sell at cost price but uses a faulty weight (say 900g instead of 1000g). This automatically gives him a profit. You need to calculate that hidden profit percent.

• Profit% = (True weight - False weight) / False weight x 100
• The dealer sells less but charges for more, so profit is on the false measure
• If the dealer also adds a markup, apply both effects
• Think of it as: he gets paid for 1000g but gives only 900g

Two Items Sold at Same SP — Classic Trap

A very frequent RRB NTPC pattern: two items sold at the same price, one at x% profit and another at x% loss. Instinct says net result is zero, but it is always a net LOSS. This is a guaranteed question in many papers.

• When two items sold at same SP with equal profit% and loss%, there is always a net loss
• Net Loss% = (Common %)^2 / 100
• The loss is always on the total CP, not SP
• This formula works ONLY when both percentages are equal

• Calculating profit% or loss% on SP instead of CP — always use CP as the base for percentage
• Adding two successive discounts directly (20% + 10% = 30%) instead of using the formula — actual is 28%
• Thinking equal profit% and loss% on same SP cancels out — it always results in a net loss of x^2/100%
• Confusing Markup (on CP) with Discount (on MP) — both percentages apply on different bases
• In faulty weight problems, putting (True - False) over True weight instead of False weight — denominator is False weight

• PLC Rule: Profit and Loss percentages are always on CP. Discount is always on MP. Remember PLC = Percent on Lower Cost, Discount on Marked.
• Same SP trick: Same price, same percent = SAD (Sad outcome = always a loss). Loss% = square of that percent divided by 100.
• Successive discounts: Use the formula a + b - ab/100. Think of it as: you get less than the sum because the second discount bites into an already reduced price.
• Faulty weight profit: Think Shopkeeper Cheats, so Profit = Extra he keeps / What he actually gives = (True - False) / False x 100.

• RRB NTPC typically has 2-3 questions from Profit and Loss per stage. Difficulty is easy to moderate — mostly direct formula application with one tricky question on successive discounts or faulty weights.
• The two-item same SP question (one profit one loss) appears in almost every RRB paper — memorize the x^2/100 formula and never waste time re-deriving it.
• Questions often mix CP, MP, and SP in a single problem — read carefully which price is being asked for and which is given.
• Time-saving trick: For quick CP calculation, use the multiplier method. SP = CP x (100 + P%)/100 means CP = SP / multiplier. For 20% profit, multiplier = 1.2, so CP = SP/1.2.
• Dishonest dealer questions are 1-2 lines long but test the faulty weight formula — expect at least one such question in the exam. Practice the formula until it feels automatic.