Arithmetic and Numerical Ability
Arithmetic and Numerical Ability tests school-level calculation with speed and unit discipline. Recurring areas are percentage, ratio and proportion, average, profit and loss, simple and compound interest, time-speed-distance, time and work, mensuration and simplification.
Core rules
- Percentage change: change divided by original, multiplied by 100.
- Successive change: two successive changes of a% and b% give a net change of a + b + ab/100. Do not simply add.
- Average: sum divided by count. For consecutive numbers, the average is the middle value.
- Speed: convert km/h to m/s by multiplying by 5/18.
- Train problems: a pole is crossed in train length divided by speed; a platform is crossed in train length plus platform length divided by speed.
- Mensuration: area of a rectangle is length times breadth; circumference of a circle is 2 pi r.
Worked example
A 120 m train runs at 54 km/h. How long does it take to pass a pole? Reasoning: 54 km/h = 54 x 5/18 = 15 m/s. The pole has no length, so distance = 120 m. Time = 120/15 = 8 seconds. Answer: 8 seconds.
Traps that cost marks
- Forgetting to convert km/h to m/s.
- Adding successive discounts instead of using the successive-change formula.
- Using the wrong base in percentage questions.
- Mixing radius and diameter in circle problems.
Estimate first, then calculate. If the answer choices are far apart, approximation saves time without losing accuracy.