Percentage, Ratio & Average Made Easy
A from-scratch, exam-focused guide to percentage-fraction conversions, dividing in a ratio, and averages for RRB NTPC — with memory tables, fully worked examples, and speed shortcuts to grab easy Maths marks in the CBT.
By the PadhoDost Team · 📖 7 min read · Updated 4 August 2026
Part of Railway Exams (RRB) prep🧠 One family function, three maths ideas
Picture a family wedding. When your uncle says "80% of the guests have arrived", that's a PERCENTAGE. When your mother splits 300 laddoos among three cousins in a 1:2:3 share, that's a RATIO. When you work out the average gift amount, that's an AVERAGE. You already use all three every day, Dost. In RRB NTPC we just do it faster and on paper.
In the NTPC CBT-1 you face 100 questions in 90 minutes, and Mathematics has 30 of them. That is under a minute per question. Percentage, Ratio and Average are the friendliest, most repeated topics in this section, so getting them fast and accurate is like collecting easy marks before the tricky ones arrive. Let us build the method step by step.
Part 1: Percentages (thinking in 'out of 100')
'Per cent' literally means 'per hundred'. So 45% just means 45 out of every 100. The magic word in most questions is 'of' — whenever you see 'of', it means multiply. So '45% of 500' means take 45 out of every 100, applied to 500.
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% (33 1/3%) |
| 2/3 | 66.67% (66 2/3%) |
| 1/4 | 25% |
| 3/4 | 75% |
| 1/5 | 20% |
| 1/6 | 16.67% (16 2/3%) |
| 1/8 | 12.5% |
| 1/10 | 10% |
| 1/20 | 5% |
📝 Worked example: a sale price
A shirt costs Rs 800. In a sale the price is cut by 20%. Find the new price.
Step 1: Turn the percentage into a fraction. 20% = 1/5.
Step 2: Find the cut. 1/5 of 800 = 800 / 5 = Rs 160.
Step 3: Subtract from the original. 800 - 160 = Rs 640.
Answer: the new price is Rs 640.
Part 2: Ratios (dividing things fairly)
A ratio like 2:3 tells you how a whole is shared in parts — 2 parts for one, 3 parts for the other. The trick is simple: add up all the parts to get the total number of parts, find the value of ONE part, then multiply for each share. A ratio has no units, so always convert quantities to the same unit before writing the ratio.
📝 Worked example: sharing a bonus
Divide Rs 6000 among three workers A, B and C in the ratio 2:3:5.
Step 1: Add the parts. 2 + 3 + 5 = 10 total parts.
Step 2: Find one part. 6000 / 10 = Rs 600 per part.
Step 3: Multiply for each share. A = 2 x 600 = 1200, B = 3 x 600 = 1800, C = 5 x 600 = 3000.
Step 4: Check by adding back. 1200 + 1800 + 3000 = 6000. Correct.
Part 3: Averages (the middle value)
📝 Worked example: the missing number
The average of 6 numbers is 20. A 7th number is added and the average rises to 22. Find the 7th number.
Step 1: Sum of the first 6 = Average x Number = 20 x 6 = 120.
Step 2: Sum of all 7 = 22 x 7 = 154.
Step 3: The new number = new total - old total = 154 - 120 = 34.
Answer: the 7th number is 34.
Exam shortcuts to lock in
- ✓Learn the fraction–percentage table by heart — it turns percentages into instant divisions (e.g. 25% means 'divide by 4').
- ✓'of' always means multiply: x% of N = (x/100) x N.
- ✓To divide in ratio a:b:c, one part = Total / (a+b+c), then multiply each part.
- ✓Sum = Average x Number is the master trick for almost every average problem.
- ✓Keep all quantities in the same unit before forming a ratio; ratios themselves have no unit.
- ✓Marking is +1 right, -1/3 wrong. Attempt when you can solve in about 40-50 seconds; skip pure guesses to protect your score.
⚡ Quick check
Divide Rs 960 between A and B in the ratio 5:7. How much does B receive?
Ready to test yourself? 🎯
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