UP Police Constable · Bite-size lessons

Discount

About 7 min · Numerical & Mental Ability · English

Time worked out from the lesson's 566 words at 150 words a minute, plus a minute for each question.

This topic tests your understanding of how merchants offer price reductions and how financial institutions handle bills before their due date. You must master three core concepts: marked price and trade discount (straightforward percentage reduction), true discount (the difference between a future sum and its present value at simple interest), and banker's discount (simple interest on the face value of a bill). Successive discount problems — where multiple percentage reductions apply one after another — require careful calculation to avoid errors.

Key ideas

• Marked Price (MP) is the labeled or list price before any discount. Selling Price (SP) is what the customer actually pays after discount is applied. The relationship is: SP = MP − Discount.
• Discount Percentage is always calculated on the marked price unless otherwise specified. If a 25% discount is offered on MP of ₹800, discount amount = 25% of 800 = ₹200, so SP = ₹600.
• True Discount (TD) is the simple interest on the present value (PV) of a sum due at a future date. Formula: TD = (PW × R × T)/100, where PW is present worth. Also, TD = Amount − PW, and PW = (Amount × 100)/(100 + R × T).
• Banker's Discount (BD) is the simple interest on the face value (amount) of a bill for the unexpired time. Formula: BD = (Amount × R × T)/100. Banker's discount is always greater than true discount because it's calculated on the larger face value rather than present worth.
• Relationship between BD and TD: BD − TD = SI on TD. This means BD = TD + (TD × R × T)/100. Also, Amount = (BD × TD)/(BD − TD).

Watch out for

• Adding successive discounts directly: Students often add 20% + 10% = 30% and apply 30% discount on the original price. Wrong! Each discount applies to the reduced price after the previous discount. Always use the formula or apply step-by-step.
• Confusing BD with TD: Banker's discount is SI on the face value (amount), while true discount is SI on present value. BD is always larger than TD. If a question asks for "discount on a bill," it typically means banker's discount unless specified otherwise.
• Forgetting time conversion: When time is given in months, students often use it directly in formulas meant for years. Always convert months to years (divide by 12) before applying SI-based discount formulas.

Quick reference

• Discount = MP − SP; Discount% always on MP unless stated otherwise.
• Successive discounts: Use d₁ + d₂ − (d₁d₂)/100, not d₁ + d₂.
• True Discount (TD) = (Amt × R × T)/(100 + RT); calculated on present value.
• Banker's Discount (BD) = (Amt × R × T)/100; calculated on face value; BD > TD always.
• BD − TD = SI on TD; Amount = (BD × TD)/(BD − TD).

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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