Numerical Reasoning
Shared numerical reasoning
This guide practises percentages,ratios,averages,rates,unit conversions andnumber series as shared Ghana police aptitude foundations. It does not transfer a fire-service official paper format or recruitment rule. Set up quantities and assumptions carefully before computing, and verify that the result answers the question actually asked.
Core rules to have automatic
- Order of operations: work brackets first, then powers and roots, then × and ÷ left to right, then + and −.
- Percentage change: use multipliers. +20% = ×1.20; −15% = ×0.85. Successive changes multiply, so +20% then −20% gives ×0.96, a net 4% fall, not zero.
- Ratio and proportion: scale both parts by the same factor. To split a total in ratio a:b, the total represents a+b parts.
- Averages: total = average × count. When a new value is added, the new total is the old total plus the new value.
- Rates: combine rates by adding or subtracting the work done per unit time; never average the times directly.
- Series: test first differences, then second differences, then ratios; check for alternating or two interleaved sequences.
Worked example
A 240-litre tank is filled by pipe A in 6 hours and emptied by pipe B in 8 hours. With both open, how long does the tank take to fill?
A fills 240 ÷ 6 = 40 litres per hour. B empties 240 ÷ 8 = 30 litres per hour. Net rate = 40 − 30 = 10 litres per hour. Time = 240 ÷ 10 = 24 hours. The trap is to average 6 and 8 and answer 7 hours; rates combine additively, but times do not.
Traps that cost marks
- Adding percentage changes instead of multiplying them.
- Using the original value as the denominator when the question asks for change relative to the new value.
- Mixing units (minutes with hours, grams with kilograms) before calculating.
- Solving a series with the first pattern found without checking it against every term.
- Rounding early; keep full precision until the final line.