Arithmetical and Numerical Ability: Percentages, Ratios, Work, Speed and Interest
Arithmetical and Numerical Ability checks speed and accuracy on school-level mathematics: number system, HCF–LCM, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed–distance–time, mensuration and data interpretation.
Rules to hold
- Learn fraction equivalents: 12.5% = 1/8, 16⅔% = 1/6, 20% = 1/5, 25% = 1/4 - most percentage sums then collapse into multiplication.
- Successive percentage change of a% then b%: net change = a + b + ab/100.
- Profit and loss are calculated on cost price; discount is calculated on marked price.
- Time and work: take total work as the LCM of the given days; add rates for "together", subtract for a leak or an opposing agent.
- Speed: km/h × 5/18 = m/s. A train crossing a pole covers its own length; crossing a platform covers its own length plus the platform.
- SI = PRT/100; CI = P(1 + r/100)^n − P.
Worked example
A finishes a job in 12 days and B in 18. Working together, in how many days? Take total work = LCM(12, 18) = 36 units. A does 36/12 = 3 units a day, B does 36/18 = 2 units a day. Together 5 units a day, so 36/5 = 7⅕ days. Sanity check: the answer must fall between 6 days (12/2) and 12 days.
Traps
- Solving a percentage question on the wrong base - cost price versus selling price versus marked price.
- Reversing efficiency ratios: twice as efficient means half the time, not double.
- Forgetting unit conversion when speed is given in km/h and distance in metres.
- In compound interest, computing only the first year and stopping.