Percentageप्रतिशतquestions and answersप्रश्न और उत्तर
Percentage is the language of almost every quant topic: profit, interest, data interpretation and growth all reduce to it. Get fast here and every other chapter speeds up.
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2subtopicsउप-टॉपिक
SSC CGL ~2
IBPS PO ~2
TCS NQT ~2
Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।
How percentage worksप्रतिशत को समझिए
A percentage is a fraction with denominator 100. The trick for speed is to think in fractions: 25% is a quarter, 12.5% is an eighth, 16.67% is a sixth.
When two changes happen one after another, the second acts on the new value, not the original. That is why a 10% rise followed by a 10% fall leaves you 1% below where you started.
For “A is r% more than B, so B is how much less than A?”, the base changes. Divide the same difference by the bigger number.
Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 40 cases✓ 40 मामलों पर जाँची गई
Rise by 1/n, fall by 1/(n + 1)
Use it when:कब इस्तेमाल करें: “Price rises by x%. By how much must consumption fall to keep spending the same?” or “by what % must it fall to get back?”
Write the rise as a unit fraction 1/n (25% = 1/4, 20% = 1/5, 12.5% = 1/8).
The fall that cancels it is 1/(n + 1) (1/5 = 20%, 1/6 = 16.67%, 1/9 = 11.11%).
Exampleउदाहरण
Sugar costs 25% more. By what % must a family cut consumption to spend the same?
→ 25% = 1/4 → cut 1/5 = 20%.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: (1 + 1/n) × (1 − 1/(n + 1)) = ((n + 1)/n) × (n/(n + 1)) = 1, so the two changes cancel exactly.
Limits:सीमाएँ: Works directly for unit fractions. For other rises use r/(100 + r) × 100 (a 30% rise needs a 300/13 ≈ 23.08% cut).
Formulaसूत्रRarely taughtकम सिखाई जाने वाली✓ Checked on 810 cases✓ 810 मामलों पर जाँची गई
Three successive changes in one line
Use it when:कब इस्तेमाल करें: Three changes in a row (population over three years, three discounts, or price × quantity × tax).
Net % = (a + b + c) + (ab + bc + ca)/100 + abc/10,000.
Use negative numbers for falls. For small changes the last term is usually tiny and can be dropped when options are far apart.
Exampleउदाहरण
Population grows 10%, 10% and 10% in three years. Net growth?
→ 30 + 3 + 0.1 = 33.1%
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: (1 + a)(1 + b)(1 + c) − 1 expanded gives a + b + c + ab + bc + ca + abc (with a, b, c as fractions); converting to percentages gives the formula.
Limits:सीमाएँ: Exact for any values. The last term matters when the changes are large (e.g. 50% three times: 150 + 75 + 12.5 = 237.5%).
Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 5 cases✓ 5 मामलों पर जाँची गई
Turn every % into a fraction multiplier, then cancel
Use it when:कब इस्तेमाल करें: Any chain of increases, decreases, discounts or taxes.
Rewrite each change as a fraction: +20% → 6/5, −25% → 3/4, +12.5% → 9/8, −10% → 9/10.
Multiply the fractions and cancel before computing anything.
Exampleउदाहरण
Marked 20% above cost, sold at 25% discount. Profit or loss?
→ 6/5 × 3/4 = 18/20 = 9/10 → 10% loss.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Each percentage change multiplies the value by (1 ± r/100); a fraction is just that multiplier written exactly, and products of fractions cancel.
Limits:सीमाएँ: Best when the percentages are “fraction friendly” (multiples of 5, 12.5, 16.67, 33.33). For 17% or 23% use the decimal 1.17 / 0.77.
Exam strategyपरीक्षा रणनीतिRarely taughtकम सिखाई जाने वाली✓ Checked on 49 cases✓ 49 मामलों पर जाँची गई
Round in opposite directions, and only as much as the options allow
Use it when:कब इस्तेमाल करें: Approximation questions and DI with long numbers.
Look at the gap between the two closest options as a % of the answer.
Your total rounding error (roughly the sum of each number’s % rounding) must stay well below that gap.
Round one number up and the next one down so the errors cancel.