Mathematics: Arithmetic and Numerical Ability
This section tests arithmetic and numerical ability: percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, speed–distance–time, mensuration and data interpretation. Most questions are direct if the base quantity is identified correctly, so write the base before calculating.
Core rules
- Percentage: part = base × rate/100. A percentage increase then decrease is not zero; use successive change a + b + ab/100 with signs.
- Profit/loss is always on cost price unless stated; discount is always on marked price.
- Simple interest = P × R × T / 100; compound interest = P[(1+R/100)^T − 1].
- Average = sum of values / number of values; if every value rises by k, the average rises by k.
- Time–work: work rates add; if A alone takes x days, one day’s work is 1/x.
Worked example
A trader marks an item 25% above cost and allows a 20% discount. Find profit percent. Take cost price = ₹100. Marked price = ₹125. Discount = 20% of 125 = ₹25. Selling price = ₹125 − ₹25 = ₹100. Profit = 100 − 100 = ₹0, so profit = 0%. Using successive change: +25 − 20 + (25 × −20)/100 = 0%.
Traps
- Applying discount to cost price instead of marked price.
- Mixing ratio order: a 3:2 mixture is not 2:3.
- Forgetting unit conversion in speed problems (km/h to m/s: multiply by 5/18).
- In compound interest, adding simple interest each year instead of interest on interest.