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NDA Simple Interest

Study Material — 5 PYQs (2018–2022) · Concept Notes · Shortcuts

NDA Simple Interest is a frequently tested subtopic — 5 previous year questions from 2018–2022 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2022
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Previous Year Questions

NDA Simple Interest — Past Exam Questions

5 questions from actual NDA papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the simple interest earned after 3 years?

Exam Q 22022Previous Year Pattern

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned after 3 years?

Exam Q 32022Previous Year Pattern

At what rate per annum will ₹2,400 amount to ₹3,120 in 3 years under simple interest?

Exam Q 42018Previous Year Pattern

A sum of ₹8,400 is lent at a simple interest rate of 12.5% per annum. In how many years will the interest amount to ₹3,150?

Exam Q 52020Previous Year Pattern

Rajesh borrowed some money at 8% per annum simple interest. After 3 years, he paid back ₹4,160 as interest. He then borrowed the same principal amount at 6% per annum simple interest for a certain number of years. If the interest earned in the second case is ₹3,120, find the difference (in years) between the two time periods.

Concept Notes

Simple Interest— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

SIMPLE INTEREST — COMPLETE EXAM GUIDE ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

CORE CONCEPT ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Simple Interest (SI) is the interest calculated ONLY on the original amount (called Principal). It does not change year to year. The interest earned each year stays the same. Think of it like this: if you lend Rs. 1000 at 10% per year, you earn Rs. 100 every single year — no more, no less. This is different from Compound Interest where interest is added to the principal each year. In Simple Interest, the base amount never changes.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ KEY RULES / PROPERTIES

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1. Interest is always calculated on the ORIGINAL principal, not on accumulated interest.

2. SI grows in a straight line — it is linear growth. 3. Rate is always per annum (per year) unless stated otherwise.

4. Time must be in YEARS. If given in months, divide by 12. If in days, divide by 365. 5. Amount = Principal + Simple Interest.

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2.Formula Block

Memorise — at least one formula appears in every paper
SI = (P × R × T) / 100
P = Principal (original amount)
R = Rate of interest per annum (%)
T = Time (in years)
Amount (A) = P + SI
Amount (A) = P × (1 + RT/100)
P = (SI × 100) / (R × T)
R = (SI × 100) / (P × T)
T = (SI × 100) / (P × R)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Where:

Derived formulas (very useful in exams):

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3.Exam Patterns

What examiners ask — read before attempting PYQs
TRICK 2 — SI as a fraction of Principal

If SI = (x/y) of Principal, then R × T = (x/y) × 100 Example: If SI = 3/5 of P, then R × T = 60. If T = 6, then R = 10%

TRICK 3 — Two-Part Sum Shortcut

A sum S is split into two parts at rates R1 and R2 for the same time T. Part 1 = S × (Total SI - S × R2 × T/100) ÷ [(R1 - R2) × T/100] Or use alligation on the effective rates to find the ratio of parts. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

4.Worked Example

Solve this step-by-step before moving on
1
Step 1

Write down values. P = 4500, R = 8, T = 3

2
Step 2

Apply formula. SI = (P × R × T) / 100 SI = (4500 × 8 × 3) / 100 SI = 108000 / 100 SI = Rs. 1080

3
Step 3

Find Amount. A = P + SI = 4500 + 1080 = Rs. 5580 Answer: SI = Rs. 1080, Amount = Rs. 5580 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — Find Rate (Trick-Based) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: A sum of money doubles itself in 12 years under Simple Interest. Find the rate of interest per annum.

1
Step 1

Money doubles means SI = P (interest earned equals the original amount).

2
Step 2

Use the doubling trick. R × T = 100 R × 12 = 100 R = 100/12 R = 8.33% = 8 and 1/3 % Answer: Rate = 8.33% per annum No heavy calculation needed. Just remember: R × T = 100 for doubling. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

5.Exam Traps

Common mistakes students make — avoid these

— THE #1 TRAP ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ STUDENTS CONFUSE AMOUNT WITH INTEREST. The question asks for Simple Interest but students calculate Amount (P + SI) and mark that as the answer. OR the question gives Amount and asks to find Principal — students forget to subtract the interest first. Always re-read the question: Does it ask for SI or for the total Amount? These are two different things.

This single mistake costs marks in almost every exam.

Key Points to Remember

  • SI = (P × R × T) / 100 — this is the master formula, memorise it first.
  • Amount = Principal + Simple Interest; never confuse the two in your answer.
  • Interest is always calculated on the ORIGINAL principal — it never changes in SI.
  • Convert time to years always: months ÷ 12, days ÷ 365 before applying formula.
  • SHORTCUT: If money doubles → R × T = 100; if triples → R × T = 200.
  • SHORTCUT: If SI = (x/y) of Principal, then R × T = (x/y) × 100.
  • SHORTCUT: Time to become N times = (N−1) × 100 / R years.
  • Derived formula for Rate: R = (SI × 100) / (P × T) — use when rate is unknown.
  • SI grows linearly — equal interest is earned every year throughout the period.
  • In two-part sum problems, use alligation on rates to quickly find the ratio of parts.

Exam-Specific Tips

  • SI formula: SI = (P × R × T) / 100, where P = Principal, R = Rate per annum, T = Time in years.
  • If a sum becomes N times itself at Simple Interest, then R × T = (N − 1) × 100.
  • A sum doubles at SI when R × T = 100. Example: at 10% per annum, it doubles in exactly 10 years.
  • If time is given in months, divide by 12 to convert to years before applying the SI formula.
  • If SI equals one-fourth of the Principal and Rate equals Time, then R = T = 5% and 5 years respectively.
  • The relationship between SI and Amount: A = P(1 + RT/100) — this is a single-step formula for Amount.
  • SSC CGL frequently tests the scenario where SI is a given fraction of Principal to find Rate or Time using R × T = fraction × 100.
  • In SSC exams, when two different rates are given for two parts of a sum, the alligation method on rates gives the ratio of the two parts directly.
Practice MCQs

Simple Interest — Practice Questions

53graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 53

All MCQs →
Practice 1easy

Rahul borrowed ₹12,000 at 5% simple interest per annum. If he paid ₹15,000 as total amount after some years, how many years did he borrow the money for?

Practice 2easy

A sum of money doubles itself in 5 years at simple interest. What is the rate of interest per annum?

Practice 3easy

A sum of money becomes ₹9,600 in 2 years and ₹12,000 in 4 years at simple interest. What is the principal?

Practice 4easy

A principal amount becomes ₹10,500 in 2 years and ₹12,000 in 4 years at simple interest. What is the principal amount?

Practice 5easy

A principal of ₹8,000 earns ₹1,600 as simple interest in 4 years. What is the rate of interest per annum?

Practice 6easy

At what rate of simple interest per annum will ₹2,400 amount to ₹3,120 in 5 years?

Practice 7easy

A principal amount becomes ₹8,400 after 4 years at 10% simple interest per annum. What was the original principal?

Practice 8easy

At what rate of simple interest per annum will ₹8,000 amount to ₹9,600 in 2 years?

Practice 9easy

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned after 3 years?

Practice 10easy

The simple interest on ₹8,000 for 2.5 years at a certain rate is ₹2,000. What is the rate of interest?

Practice 11easy

At what rate of simple interest per annum will ₹8,000 amount to ₹10,400 in 4 years?

Practice 12easy

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the total amount after 3 years?

Practice 13easy

Rajesh invested ₹8,000 at a simple interest rate of 12% per annum. How much interest will he earn in 3 years?

Practice 14easy

A principal amount becomes ₹6,500 in 2 years and ₹7,500 in 4 years at simple interest. What is the principal amount?

Practice 15easy

In how many years will ₹6,000 become ₹7,800 at a simple interest rate of 6% per annum?

Practice 16easy

In how many years will ₹5,000 amount to ₹6,800 at 12% per annum simple interest?

Practice 17easy

Rajesh borrowed ₹12,000 at 5% simple interest per annum. If he paid ₹2,400 as interest, for how many years did he borrow the money?

Practice 18medium

The simple interest on a certain sum for 3 years at 8% per annum is ₹2,400. What will be the simple interest on the same sum for 5 years at 6% per annum?

Practice 19medium

A sum of money becomes ₹9,240 in 4 years at 8% per annum simple interest. What was the original principal?

Practice 20medium

A person invests ₹5,000 in two parts at 6% and 9% p.a. simple interest respectively. If the total interest earned in 2 years is ₹810, how much was invested at 9% p.a.?

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60-Second Revision — Simple Interest

  • Formula: SI = (P × R × T) / 100 and Amount = P + SI — write this first in rough work.
  • Remember: Time MUST be in years — convert months by dividing by 12, days by dividing by 365.
  • Shortcut: Money doubles → R × T = 100; triples → R × T = 200; N times → R × T = (N−1) × 100.
  • Shortcut: SI = fraction of P? Just multiply that fraction by 100 to get R × T directly.
  • Trap: Always check — does the question ask for SI or Amount? These are NOT the same. SI = A − P.
  • Derived formulas: P = (100 × SI)/(R × T), R = (100 × SI)/(P × T), T = (100 × SI)/(P × R).
  • Two-part sum problems: Use alligation on the two interest rates to find the ratio of the two parts quickly.
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