Quant Shortcuts for SSC and Banking: Percentages, Ratio and Interest
Fraction–percentage tables, the successive change formula, shortcuts for interest, ratio and work problems, each with a worked example you can check.
By the World MCQ Forum India Editorial Team · 27 October 2026 · 3 min read
Speed in Quantitative Aptitude doesn’t come from tricks you can’t explain. It comes from knowing a small number of relationships so well that you stop calculating them. Every shortcut on this page has a worked example, so you can check it yourself.
1. Know these fractions as percentages
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 1/9 | 11.11% |
| 1/4 | 25% | 1/10 | 10% |
| 1/5 | 20% | 1/11 | 9.09% |
| 1/6 | 16.67% | 1/12 | 8.33% |
| 1/7 | 14.29% | 1/16 | 6.25% |
Example: 37.5% of 640. Since 37.5% = 3/8, the answer is 640 × 3 ÷ 8 = 240.
2. Successive percentage changes
Two changes of a% and b% (use minus for a decrease) equal a single change of:
a + b + (a × b) ÷ 100
Example: a price rises 20% and then falls 10%. Net change = 20 − 10 + (20 × −10) ÷ 100 = 10 − 2 = +8%.
Successive discounts work the same way: 20% and 10% off equal 20 + 10 − 2 = 28% off, not 30%.
3. “More than” versus “less than”
If A is r% more than B, then B is less than A by r ÷ (100 + r) × 100.
Example: if A earns 25% more than B, B earns 25 ÷ 125 × 100 = 20% less than A. The base changes, so the percentages differ.
4. Profit and loss
- Profit and loss percentages are always on the cost price.
- If an item is sold at a profit of p%, CP = SP × 100 ÷ (100 + p).
Example: sold for ₹1,150 at a 15% profit. CP = 1,150 × 100 ÷ 115 = ₹1,000. (Taking 15% off ₹1,150 would wrongly give ₹977.50.)
5. Interest
- Simple interest = P × R × T ÷ 100.
- For 2 years, compound interest − simple interest = P × (R ÷ 100)².
Example: on ₹8,000 at 5% for 2 years, CI − SI = 8,000 × 0.05 × 0.05 = ₹20.
- A sum doubles at simple interest in 100 ÷ R years: at 10% that is 10 years.
6. Ratio
- To share an amount in the ratio a : b, one part = amount ÷ (a + b).
- To combine A : B and B : C, make B the same in both.
Example: A : B = 2 : 3 and B : C = 4 : 5. Multiply the first by 4 and the second by 3: A : B = 8 : 12 and B : C = 12 : 15, so A : B : C = 8 : 12 : 15.
7. Time and work
If A finishes a job in a days and B in b days, together they take a × b ÷ (a + b) days.
Example: 12 days and 24 days: 12 × 24 ÷ 36 = 8 days.
For a filling pipe (a hours) and a leak (b hours), the tank fills in a × b ÷ (b − a) hours.
8. Speed and distance
- To convert km/h to m/s, multiply by 5/18. 72 km/h = 20 m/s.
- A train passing a pole covers its own length; passing a platform, its length plus the platform’s.
- For equal distances at speeds x and y, the average speed is 2xy ÷ (x + y), not (x + y) ÷ 2.
Example: 60 km/h one way and 40 km/h back: 2 × 60 × 40 ÷ 100 = 48 km/h.
Put them to work
Shortcuts only become automatic with practice. Work through our Percentage, Profit and Loss and Interest, Time and Work MCQs. Each solution shows the working, so you can see where each shortcut applies.