HireSol
← Aptitude and reasoning for placement tests

Lesson 1 of 4

Percentages, profit and loss, and interest

3 min read

Aptitude tests (TCS NQT, Infosys, Wipro, Accenture, Capgemini, AMCAT, eLitmus and company-specific tests) usually give 20–40 questions in 30–60 minutes. Speed comes from knowing patterns and shortcuts, not from long calculations.

Percentages

  • Fraction ↔ percentage table to memorise: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 ≈ 14.28%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/10 = 10%, 1/11 ≈ 9.09%, 1/12 ≈ 8.33%.
  • Successive change: a% then b% → total change = a + b + ab/100. A price rises 20% then falls 20%: 20 − 20 − 4 = −4% (a net loss).
  • If A is r% more than B, B is r/(100 + r) × 100% less than A. If A is 25% more than B, B is 20% less than A.

Example: a population of 50,000 grows 10% a year. After 2 years: 50,000 × 1.1 × 1.1 = 60,500.

Profit and loss

  • Profit % = (SP − CP) ÷ CP × 100 (always on the cost price unless stated otherwise).
  • SP = CP × (100 + profit%) ÷ 100.
  • Marked price and discount: SP = MP × (100 − discount%) ÷ 100.
  • Two articles sold at the same price, one at x% profit and one at x% loss: always a net loss of x²/100 %.

Example: a shopkeeper marks goods 40% above cost and gives a 25% discount. SP = 1.4 × 0.75 = 1.05 × CP, a profit of 5%.

Simple and compound interest

  • SI = P × R × T ÷ 100.
  • CI amount = P × (1 + R/100)ᵀ; CI = amount − P.
  • For 2 years, CI − SI = P × (R/100)².

Example: the difference between CI and SI on ₹10,000 at 10% for 2 years = 10,000 × 0.01 = ₹100.

Ratios, averages and mixtures

  • If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c = 8 : 12 : 15 (make b the same).
  • Average = sum ÷ count. If one value changes by d, the average changes by d ÷ n.
  • Alligation for mixtures: (dearer − mean) : (mean − cheaper) = quantity of cheaper : quantity of dearer.

Example: mix rice at ₹40/kg and ₹60/kg to get ₹52/kg: (60 − 52) : (52 − 40) = 8 : 12 = 2 : 3 (cheaper : dearer).

Check yourself

  • A price falls 10% and then rises 10%. Net change?
  • CP ₹800, profit 15%. What's the SP?
  • In what ratio should tea at ₹200/kg and ₹300/kg be mixed to get ₹240/kg?

Sign up free to save your progress.

Next →