Simple Interest for SSC CGL — Formula, Tricks, and PYQ Walkthrough

Concept

Simple Interest (SI) is the most transparent form of interest calculation — the interest earned each year is always the same fixed amount, calculated only on the original principal, never on accumulated interest.

Think of it like a daily-wage contract. If you lend ₹10,000 to a friend at 10% per annum, you earn ₹1,000 every single year. The second year, you still earn ₹1,000 on the same ₹10,000 — your friend doesn't owe you interest on last year's interest. That flat, predictable structure is what makes it "simple."

The core formula is:

$SI = \frac{P \times R \times T}{100}$

Where:

• P = Principal (original sum invested or borrowed)
• R = Rate of interest per annum (in %)
• T = Time (in years)

And the Amount (A) — what you get back at the end — is:

$A = P + SI = P + \frac{P \times R \times T}{100} = P\left(1 + \frac{RT}{100}\right)$

Here's what makes SSC CGL SI questions tick: they almost never just ask you to calculate SI directly. They give you two of the four variables (P, R, T, SI or A) and ask for the third or fourth. So you need all four derived forms cold:

$P = \frac{SI \times 100}{R \times T}$

$R = \frac{SI \times 100}{P \times T}$

$T = \frac{SI \times 100}{P \times R}$

The questions look different on the surface — "find the rate," "find the principal," "in how many years" — but they all reduce to one of these four forms. Once that clicks, SI becomes a one-line topic.

Deep Dive

The Base Formula and Its Four Avatars

The formula $SI = \frac{PRT}\{100\}$ is the anchor. Every SSC CGL SI question is a manipulation of this single equation. Drill the derived forms until you can write them in your sleep:

| Given | Find | Formula | |---|---|---| | P, R, T | SI | $SI = \frac{PRT}\{100\}$ | | SI, R, T | P | $P = \frac{SI \times 100}{R \times T}$ | | SI, P, T | R | $R = \frac{SI \times 100}{P \times T}$ | | SI, P, R | T | $T = \frac{SI \times 100}{P \times R}$ |

Working with Amount vs. Interest

Look — a very common trap in CGL questions is giving you the Amount (A) and asking about interest or principal. The moment you see "amounts to ₹X," subtract the principal first:

$SI = A - P$

Only then plug into the formula. Students who skip this step lose a mark every time.

Example: ₹2,500 amounts to ₹3,250 in 4 years. SI = 3,250 − 2,500 = ₹750. Now find R. Done. Never try to directly substitute A into the SI formula.

The Rate-Time Interchangeability Trick

Here's something CGL setters exploit regularly: if a problem says "rate and time are equal" or gives you a constraint linking R and T, you can substitute one variable. For instance, if R = T = n, then:

$SI = \frac{P \times n \times n}{100} = \frac{Pn^2}{100}$

This creates a quadratic — but in CGL, the numbers are always clean, so just test the options.

When T is in Months or Days

Always convert before substituting:

• Months: divide by 12. (9 months = 9/12 = 3/4 year)
• Days: divide by 365 (or 360 if the question says "a year of 360 days").

Missing this conversion is a free mark lost.

Ratio-Based SI Problems

Some CGL questions state: "SI on a sum for 3 years at 5% equals SI on another sum for 2 years at 6%." These are product problems. You just equate:

$P_1 \times 3 \times 5 = P_2 \times 2 \times 6$

$15P_1 = 12P_2 \implies \frac{P_1}{P_2} = \frac{12}{15} = \frac{4}{5}$

No need to find absolute values — the ratio comes directly from the product of R and T.

Difference Between SI and Compound Interest (CI) Over 2 Years

This is a bridge topic that regularly appears in CGL. For 2 years at rate R% on principal P:

$CI - SI = P \times \left(\frac{R}{100}\right)^2$

Know this. It lets you solve CI-vs-SI comparison questions without computing CI from scratch.

Installment-Type SI Problems

Occasionally CGL will ask: "A sum is split into two parts; one earns SI at r₁% and another at r₂%; total interest is ₹X — find the parts." Use the weighted average / alligation approach:

$\frac{\text{Part}_1}{\text{Part}_2} = \frac{r_2 - r_{avg}}{r_{avg} - r_1}$

Where $r_{avg}$ is the effective rate derived from total interest and total principal.

Memory Tricks & Shortcuts

Fast-Solving Framework

When you see an SI question in the exam hall, run this decision tree in order:

Step 1 — Identify what's given and what's asked. Tag each number: is it P, R, T, SI, or A?

Step 2 — Is "amount" mentioned? If yes, extract SI = A − P before anything else. Non-negotiable.

Step 3 — Is T in months or days? Convert to years immediately.

Step 4 — Which formula avatar do you need?

• Find SI → use $\frac{PRT}\{100\}$
• Find P → use $\frac{SI \times 100}{RT}$
• Find R → use $\frac{SI \times 100}{PT}$
• Find T → use $\frac{SI \times 100}{PR}$

Step 5 — Does the answer match an option? If not, check whether you subtracted A−P, check unit conversion, and verify you didn't use Amount where SI was needed.

Total time target: straightforward SI question in 25−35 seconds. If you're past 45 seconds, substitute options instead of computing.

Solved PYQs

Why this question: Direct SI calculation — the most fundamental question type. Tests whether you can execute PRT/100 cleanly without errors.

Solving path: P = 5,000, R = 8, T = 3. SI = (5000 × 8 × 3) / 100 = 120,000 / 100 = ₹1,200. Using decimal multiplier: 8% × 3 = 24% of 5,000 = ₹1,200. Both routes under 20 seconds.

Why this question: Tests reverse calculation — "find the rate." The Amount-to-SI extraction step is the critical first move here.

Solving path: Step 1 — extract SI: 3,250 − 2,500 = ₹750. Step 2 — R = (750 × 100) / (2,500 × 4) = 75,000 / 10,000 = 7.5%. Check options — 7.5% is there. Done in ~25 seconds.

Why this question: Classic "find the principal" — tests the inverted formula under time pressure.

Solving path: P = (840 × 100) / (6 × 2) = 84,000 / 12 = ₹7,000. The division 84,000 ÷ 12 — think of it as 84,000 ÷ 12 = 7,000 directly (12 × 7 = 84). No long division needed.

Why this question: Tests the "find time" variant — the least practiced of the four formula avatars, which is exactly why it shows up on CGL.

Solving path: SI = 9,100 − 6,500 = ₹2,600. T = (2,600 × 100) / (6,500 × 10) = 260,000 / 65,000 = 4 years. Simplify before multiplying: 2,600/6,500 = 4/10, then 4/10 × 100/10 = 400/100 = 4. Cleaner mental arithmetic.

Why this question: Combines finding SI and then computing Amount — two steps, one question. Tests whether you know Amount = P + SI.

Solving path: SI = (12,000 × 7.5 × 2) / 100. Compute 12,000 × 7.5 = 90,000. Then 90,000 × 2 = 180,000. Divide by 100 = ₹1,800. Amount = 12,000 + 1,800 = ₹13,800. Using decimal multiplier: 7.5% × 2 = 15% of 12,000 = ₹1,800. Same answer, slightly faster mental path.

Common Mistakes

• Using Amount instead of SI in the formula. The formula needs SI, not A. If the question says "amounts to ₹X," you must subtract the principal first. This is the single most common error on SI questions — and it costs a quarter-mark from the wrong option selected.

• Forgetting to convert time units. If T is given in months, dividing by 12 is mandatory before substituting into PRT/100. Substituting "9" when you should substitute "0.75" produces an answer 12 times too large.

• Treating Rate as a decimal without adjusting the formula. The formula PRT/100 already assumes R is in percent. Do not write R = 0.08 and also divide by 100. Either use R = 8 with the /100, or use R = 0.08 without the /100. Mixing these gives an answer 100 times off.

• Confusing SI with Amount in the answer options. CGL setters deliberately include both SI and Amount as options in the same question. If you calculated SI but the question asks for Amount, you will find your SI value as one of the wrong options. Always re-read what exactly is being asked.

• Computing R×T products in the wrong order when ratios are involved. In ratio-based questions (two sums, two rates, two times, equal interest), the equation is P₁R₁T₁ = P₂R₂T₂. Students sometimes flip a ratio and lose it. Write the equation out explicitly before simplifying.

• Assuming "rate" means annual when it isn't stated. CGL questions occasionally specify "per month" or "half-yearly." If the rate unit isn't annual, convert T to the same unit as R before applying the formula.

Related Topics

• compound interest
• percentage
• ratio proportion
• profit loss
• time work
• averages

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