Discount — Study Notes for UP Police Constable

Overview

Discount questions are a staple of the Numerical Ability section in UP Police Constable exams, typically appearing in 3–5 questions per paper. 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 — are particularly common and require careful calculation to avoid errors.

Unlike profit-loss problems that focus on cost price versus selling price, discount problems center on **marked price (MP)**, **selling price (SP)**, and various discount types. The exam favors practical scenarios: shopkeepers announcing "20% off," banks discounting bills 6 months early, or festival sales with "buy one get 40% off the second item." Strong command of percentage calculations and the relationship between present value, future value, time, and rate of interest will serve you well here. Expect both direct calculation questions and word problems requiring 2–3 steps.

Most importantly, distinguish clearly between true discount (TD) and banker's discount (BD) — confusing these definitions is the most common error students make. Practice converting time periods (months to years) and applying formulas accurately under time pressure.

Key Concepts

• **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).

• **Successive Discounts** are multiple discounts applied one after another, not added together. If discounts are d₁% and d₂%, the single equivalent discount = d₁ + d₂ − (d₁ × d₂)/100. For three discounts d₁%, d₂%, d₃%, apply the formula twice sequentially.