Simple Interest (साधारण ब्याज) is the most direct way to calculate the cost of borrowing money — or the return on lending it. The core idea is this: interest is charged only on the original principal, every single year, at a fixed rate. It never compounds, never snowballs.
Think of it like a daily-wage worker getting paid a flat ₹500 every day regardless of how many days he has already worked. Day 1 = ₹500. Day 10 = ₹500. Day 100 = ₹500. The wage never changes because of accumulated days. Similarly, in Simple Interest, the interest for Year 3 is exactly the same as Year 1 — because it is always calculated on the same principal.
This makes Simple Interest linear. Plot it on a graph and you get a straight line. That linearity is exactly why UP Police Constable paper loves it — the calculations are clean, they fit in a 60-second window, and the traps are predictable (more on those in Common Mistakes).
Three variables drive everything:
Everything in this chapter is a rearrangement of one formula. Once that formula is in your muscle memory, you stop "solving" these questions — you just read and write.
A real-world analogy: the government's Kisan Credit Card or a moneylender in a village often charges simple interest. If you borrow ₹10,000 at 10% per annum for 2 years, you owe ₹2,000 extra at the end — ₹1,000 per year, flat. No interest on interest. That is Simple Interest.
And the total amount received or repaid:
These two lines contain every Simple Interest question on any government exam. The rest is just algebra — isolating whichever variable is unknown.
| Unknown | Formula | |---|---| | SI | | | P | | | R | | | T | |
You do not need to memorise all four. Memorise the triangle method: write P, R, T in a triangle, multiply across the bottom (P × R × T), divide by 100 to get SI. Then cover whatever you want to find, and the triangle tells you what to divide into what.
This is the most exam-relevant variant. When a question says "a sum becomes N times," you must immediately translate:
This is because Amount = P + SI, so SI = Amount − P = NP − P = (N − 1)P.
Now plug into the SI formula:
Cancel P from both sides:
So:
Look at how clean this is. If a sum triples (N = 3) in 25 years:
If a sum becomes 4 times (N = 4) in 20 years:
Both of these are actual PYQs from 2024. The pattern is identical.
When a question says "it becomes 3 times at 5%, at what rate will it become 6 times in the same time?" — here is the clean approach:
Step 1: Find T from the first condition. → years
Step 2: Use T in the second condition. →
The key insight: T stays fixed. You find T from condition 1, then plug into condition 2.
These appear regularly. The logic is simple:
If A lends ₹30,000 at 10% for 5 years, total due = 30,000 + 15,000 = ₹45,000. B pays ₹40,000 cash + a watch. Watch value = ₹45,000 − ₹40,000 = ₹5,000.
One trap the paper sets: mixing months and years, or giving rate as "per month" when you expect "per annum." Always check:
Draw an inverted triangle. Write SI at the top. Below it, on the left write P×R×T, and on the right write 100. To find SI: multiply P, R, T and divide by 100. To find any of P, R, or T: SI × 100, then divide by the product of the other two. This visual takes 2 seconds to recall versus hunting through rearranged formulas. Standard rearrangement time: 20s. Triangle recall: 3s.
When a sum becomes N times: immediately write R × T = 100 × (N − 1). Don't set up the full SI equation. For "triples in 25 years": R × 25 = 100 × 2 = 200, so R = 8%. You skip two algebraic steps. Standard method: set up SI = 2P, substitute, cancel P, isolate R — 4 steps. Shortcut: one multiplication, one division — 2 steps. Time saved: roughly 25 seconds per question.
Compute R × T first. This gives you "what percentage of P is the SI." For ₹37,500 at 2% for 4 years: R × T = 8. So SI = 8% of 37,500 = 8 × 375 = ₹3,000. You never write the fraction 37500 × 2 × 4 / 100. Instead, 2 × 4 = 8, then 1% of 37500 = 375, then 8 × 375 = 3,000. Standard full-product method: 6 digit-multiplication steps. This shortcut: 3 steps. Saves 15-20 seconds.
Instead of finding SI first and then adding P, compute the multiplier directly. P = ₹6,000, R = 12%, T = 2 years. Multiplier = 1 + (12 × 2)/100 = 1 + 0.24 = 1.24. Amount = 6000 × 1.24 = ₹7,440. No intermediate SI calculation needed. Standard two-step method: calculate SI = ₹1,440, then add ₹6,000. One-shot: single multiplication. Eliminates one addition step, reduces carry errors.
When a sum becomes X times at rate R, and the question asks what rate makes it Y times in the same time: the SI needed changes from (X−1)P to (Y−1)P, while T stays fixed. So the new rate = R × (Y−1)/(X−1). For "3 times at 5%, same T, becomes 6 times": new rate = 5 × (6−1)/(3−1) = 5 × 5/2 = 12.5%. No need to find T at all. Standard method: find T (2 steps), substitute into new equation (2 steps). This shortcut: 1 ratio multiplication. Saves 30 seconds.
When you see a Simple Interest question in the exam hall, run this decision tree in 5 seconds:
Step 1 — What type is this?
Step 2 — Units check. Is time in months? Is rate monthly? Convert before touching the formula.
Step 3 — Which variable is missing? Isolate it using the triangle. SI × 100 on top, product of the other two below.
Step 4 — Arithmetic shortcut. Compute R × T first, then take that percentage of P using 1% anchor.
If any answer option looks wildly off — say, an amount less than the principal — eliminate immediately without calculation. This alone saves 10-15 seconds on badly-set traps.
Why this question: Tests the basic Amount = P + SI formula and the one-shot multiplier approach. Most common question type in UP Police Constable.
Solving path: R × T = 12 × 2 = 24. So SI = 24% of 6,000 = ₹1,440. Amount = 6,000 + 1,440 = ₹7,440. Or one-shot: 6,000 × 1.24 = ₹7,440. Eliminate option C (₹6,000) immediately — that would mean zero interest.
Why this question: Hindi-language SI question — tests whether you read मूल राशि (principal), दर (rate), and समय (time) correctly. Pure formula application.
Solving path: R × T = 7 × 3 = 21. SI = 21% of 12,800. 1% of 12,800 = 128. 21 × 128 = 2,688. Answer: ₹2,688. Cross-check: none of the wrong options (₹2,898, ₹2,900, ₹2,709) are anywhere near a simple arithmetic slip — they are designed to catch you if you misread rate or time.
Why this question: "Becomes N times" pattern — the highest-frequency SI variant in UP Police 2024 paper.
Solving path: "Triples" → SI = 2P. Use R × T = 100 × (3−1) = 200. T = 25 years, so R = 200/25 = 8%. Direct. Do not set up the full equation with an actual value of P.
Why this question: Tests "becomes 4 times" — same pattern, different multiplier. Confirms you can generalise, not just memorise one case.
Solving path: "4 times" → SI = 3P. R × T = 100 × 3 = 300. T = 20 years. R = 300/20 = 15%. Answer is 15%. Note: option A (5%) is a trap — 5% × 20 years = 100%, which only doubles the principal, not quadruples it.
Why this question: Watch/object settlement — a recurring story-format question that students waste time on by overcomplicating.
Solving path: SI = 30,000 × 10 × 5 / 100 = ₹15,000. Total due = 30,000 + 15,000 = ₹45,000. B paid ₹40,000 cash. Remaining = ₹45,000 − ₹40,000 = ₹5,000 = price of watch. The question is linear once you compute total due first.
Why this question: Same-time rate scaling — the advanced pattern that combines two conditions. Tests whether you can link two "becomes X times" scenarios.
Solving path using scaling trick: New rate = 5 × (6−1)/(3−1) = 5 × 5/2 = 12.5%. Alternatively: 3 times at 5% means T = 40 years. For 6 times: SI needed = 5P. R = 5P × 100 / (P × 40) = 12.5%. Both routes confirm 12.5%.
Forgetting to add P to get Amount. The formula gives SI, not Amount. If the question asks "total amount received," you must compute P + SI. A surprisingly large number of wrong answers in this chapter come from selecting the SI value when Amount is asked — exactly what option A in the 2026 question tries to trap you with.
"Becomes N times" confusion. "Triples" does not mean SI = 3P. It means Amount = 3P, so SI = 2P. Every "becomes N times" question requires you to subtract 1 from N before multiplying. Writing SI = 3P when a sum triples is the single most common mistake in this chapter.
Mixing time units. If T is given in months, you must divide by 12 before plugging into the formula. Plugging in months directly into a formula that expects years inflates your answer by a factor of 12. Check units before every calculation.
Using the wrong base for rate. If rate is given as "per month," it cannot be plugged in as-is when T is in years. The standard formula assumes R is per annum and T is in years. When in doubt, convert rate to per annum: R_annual = R_monthly × 12.
Cancellation errors in "N times" questions. When you write (N−1)P = P × R × T / 100, you cancel P from both sides. Students sometimes carry P into the next step, leading to R = (N−1)P² × 100 / (P × T) — a nonsense expression. Cancel P immediately and completely.
The annual instalment trap. In questions like "what annual instalment discharges a debt of X in N years," the formula is not straightforward. If unsure, back-calculate from answer options: multiply the answer by N, subtract the interest it would have earned, and check if you get X. This elimination approach is faster than deriving the instalment formula from scratch under exam pressure.