Quantitative Aptitude: Multi-Step Arithmetic Under Time Pressure
What this domain rewards
SPJAT quantitative questions are short but multi-step: percentages, ratio and proportion, averages, time–speed–distance, time-and-work, simple and compound interest, permutations-combinations, and basic mensuration. No calculator is assumed, so the winning skill is converting a word problem into one clean equation and choosing numbers that cancel.
Rules worth memorising
- Successive percentage changes multiply: +20% then −20% gives 0.8 × 1.2 = 0.96, a net fall of 4%, not zero.
- Percentage change always uses the original base: new = old × (1 ± r).
- On a fixed distance, speed and time are inversely proportional: a speed ratio of 3:4 implies a time ratio of 4:3.
- Work rates add: if A finishes in a days and B in b days, together they take ab/(a+b) days.
- Compound interest: A = P(1 + r/n)^(nt). Simple interest grows linearly, so CI exceeds SI from the second year onward.
- Profit percentage is on cost price unless stated; discount is on marked price.
Worked example
A can do a job in 12 days, B in 18 days. They work together for 4 days, then B leaves. How long does A need to finish?
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36 per day. In 4 days they complete 20/36 = 5/9. Remaining work = 4/9. At A's rate of 1/12 per day, time = (4/9) × 12 = 16/3 = 5⅓ days.
Traps that cost marks
- Adding successive percentages instead of multiplying them.
- Using the new value as the base for a percentage fall.
- Forgetting unit conversion: km/h to m/s is ×5/18.
- Assuming average speed is the mean of two speeds; it is total distance divided by total time.
- Ignoring that a ratio such as 5:8 has 13 parts, not 8.