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Quantitative Abilities 2% exam weight

Percentage & Simple/Compound Interest

Part of the SSC CGL Tier 2 study roadmap. Quantitative Abilities topic ssc2-qa-003 of Quantitative Abilities.

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Percentage & Simple/Compound Interest

Concept

Percentage is a ratio expressed as a fraction of 100 — the most practical concept in SSC Quant because it’s used everywhere (profit, discount, data interpretation, statistics). The key skill is converting between fractions and percentages: 1/3 = 33.33%, 1/7 ≈ 14.28%, 1/8 = 12.5%, 1/11 ≈ 9.09%, 1/13 ≈ 7.69%. Knowing these common conversions saves time.

Simple Interest (SI) is calculated only on the original principal. Compound Interest (CI) is calculated on the accumulated amount each period. For the same principal, rate, and time: CI > SI (except in Year 1 where they’re equal). The difference between CI and SI compounds grows exponentially with time.

In Tier 2, expect questions where percentage is used to find original price after discount, population growth/depreciation, or comparing two quantities.

Key Points

  • To increase a value by x%: multiply by (100+x)/100. To decrease: multiply by (100−x)/100.
  • Two successive percentage changes (x% then y%): Net change = x + y + xy/100 (add if both increases, use sign for decreases).
  • CI formula for half-yearly compounding: rate halved, time doubled. For quarterly: rate/4, time × 4.
  • SI and CI are equal in year 1. After that, CI grows faster at positive rates.
  • Population problems: if rate is r% per year, population after n years = P × (1 + r/100)^n.

Worked Example

Q: A shopkeeper offers two successive discounts of 20% and 10% on an article priced at ₹2,500. Find the selling price. Approach: After 20% discount: 2500 × 0.80 = 2000. After 10% discount: 2000 × 0.90 = 1800. Answer: ₹1,800

SSC Pattern / Tips

  • Successive discounts are multiplicative — never add them directly. A 20% + 10% discount is NOT a 30% discount.
  • For CI with different compounding periods, adjust both rate and time proportionally.
  • Percentage questions often require finding the base — if A is x% more than B, then B = A / (1 + x/100).
  • Learn the fraction-to-percentage table for common fractions — this is a major speed booster.

📐 Diagram Reference

A timeline showing 3 years with a bar chart: two bars per year for SI and CI growth, with CI bar always taller than SI bar, widening gap over time.

Diagrams are generated per-topic using AI. Support for AI-generated educational diagrams coming soon.