Before you begin
What you need: Percentages, ratios, averages and basic work–motion formulas.
- Identify the mathematical model before calculating
- Estimate and check units to catch errors
- Review a timed test using error categories
Understand the idea
Translate before calculating
Identify the unknown and the relationship: a percentage change needs a base, a work problem needs a rate, and a crossing problem needs a distance to clear. A familiar keyword alone is not enough to select a formula.
Estimate the answer's scale
An approximate answer can expose arithmetic errors. If a price falls by 20%, the result should be near four-fifths of the original, never larger than it. Check units and whether a proposed result is possible.
Use review to improve the next attempt
Classify missed questions as concept, arithmetic, reading or time-management errors. Rework the question without a timer, write the missed rule in one sentence, and practise a similar question before retesting.
A repeatable solving routine
- Read the unknown
- Choose the model
- Estimate & solve
- Check & learn
A method you can reuse
Read → model → estimate → calculate → verify
Use the marking scheme shown for your quiz. Negative marking changes the cost of unsupported guesses.- Read the required quantity and mark the relevant numbers and units.
- Choose the model, estimate a plausible range, and solve step by step.
- Verify the result against the original question; flag time-consuming questions for a later pass when the test allows it.
Before submitting a numerical answer, perform one independent check: substitute it back, estimate its size, or confirm its units.
Worked examples
Read the question first. Try a step yourself, then compare your reasoning.
Percentages and price
A ₹1,000 item is sold at 12% profit. Find selling price.
- Identify cost price as the percentage base.
- 12% of ₹1000 = ₹120.
- SP = cost + profit = 1000 + 120.
Time and distance
A runner covers 600 m in 2 minutes. Find speed in m/s.
- Convert 2 minutes to 120 seconds.
- Speed = distance/time = 600/120.
- Check: 5 m each second gives 600 m in 120 seconds.
Review a combined-average trap
Ten students average 40 marks and thirty average 60. Find the overall average.
- A simple mean of 40 and 60 would ignore group sizes.
- Total marks = 10 × 40 + 30 × 60 = 2200.
- Divide by 40 students.
Check your understanding
Quick questions, with explanations. These are for self-study and do not affect your account score.
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Percentage Calculator
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