Arithmetic and Numerical Ability: Shortcut-Driven School Mathematics
Arithmetic and Numerical Ability in the AP Police Constable test is school-level mathematics under time pressure: percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time and work, speed and distance, mensuration and data interpretation. The paper rewards the shortcut, not the long division.
Rules worth memorising
- Successive percentage change: net change = a + b + ab/100, with signs carried.
- Simple interest: SI = P x R x T / 100; for doubling at SI, R x T = 100.
- Compound interest: A = P(1 + R/100)^T; CI minus SI for two years = P(R/100)^2.
- Time and work: take total work as the LCM of individual days, add the rates, then invert.
- Average speed over equal distances = 2xy/(x+y), never (x+y)/2.
- km/h to m/s: multiply by 5/18.
Worked example
A trader raises a price by 20% and then allows a 20% discount. What is the net effect? Reasoning: a = +20, b = -20, so net = 20 - 20 + (20 x -20)/100 = -4%. Verify with a Rs 100 base: 100 becomes 120, then 96. Net loss 4%. The trap option is 'no change'.
Traps that cost marks
- Applying the second percentage to the original base instead of the new one.
- Reading 'A is 25% more than B' as 'B is 25% less than A' (it is 20% less).
- Using simple interest when the question compounds, or compounding half-yearly (halve the rate, double the periods).
- Mixing metres with kilometres or minutes with hours in speed and mensuration items.
- In data interpretation, answering from the visual height of a bar rather than the printed value.