Percentages – SBI PO (Quantitative Aptitude)
Percent means “per hundred”.
Formula
[ % \text{ value} = \frac{\text{Part}}{\text{Whole}}\times 100 ]
1️⃣ Simple Explanation
- If 20 is 20 % of 100, then 20 % of 200 = 40, 20 % of 150 = 30, etc.
- Percentages help you compare quantities, calculate increases/decreases, and solve many exam problems.
2️⃣ Key Points (Quick Reference)
| Concept | What It Means | How to Compute |
|---|---|---|
| Percentage of a Number | p% of x |
x * p / 100 |
| Part from Whole | p% of Whole = Part |
Part = Whole * p / 100 |
| Whole from Part | Part is p% of Whole |
Whole = Part * 100 / p |
| Percentage Increase/Decrease | New value = old value ± (percentage × old value) | New = Old × (1 ± p/100) |
| Change in Percentage | % change = (New – Old)/Old × 100 |
Δ% = (Δ/Old) × 100 |
| Inverse Percentage | If x is p% of y, then y is 100/p% of x |
y = x * 100 / p |
| Equivalent Percentages | p% of x = q% of y → p/x = q/y |
x/y = p/q |
| Ratio & Percent | a:b = p%:q% → a/b = p/q |
a = k*p, b = k*q (k any positive integer) |
Common Pitfalls
- Mixing “percent” with “percentage” – use the formula consistently.
- Forgetting the “×100” step when converting from part to whole or vice‑versa.
- Assuming “increase by 20 %” means “add 20 to the number”; it actually multiplies by
1.20. - Inverting percentages incorrectly – remember
p%ofy⇒yis100/p%ofx.
3️⃣ Worked Example (SBI‑style)
Question
A shopkeeper sold a dress for ₹ 480 which is 20 % less than the marked price. What was the marked price?
Step‑by‑Step
- Identify what we know
- Sale price = ₹480
- Discount = 20 % of marked price
- Set up relation
[ \text{Sale} = \text{Marked} - 20% \text{ of Marked} ] [ 480 = M - 0.20M = 0.80M ] - Solve for (M)
[ M = \frac{480}{0.80} = 600 ] - Answer
Marked price = ₹600
Check: 20 % of 600 = 120 → 600 – 120 = 480 ✓
4️⃣ Quick Revision Summary
- Percent of a number:
x * p / 100. - Whole from part:
Whole = Part * 100 / p. - Percentage increase/decrease:
New = Old × (1 ± p/100). - Percentage change:
% change = (New – Old)/Old × 100. - Inverse percentage:
Whole = Part * 100 / p. - Ratio–percent equivalence:
a:b = p%:q%→a/b = p/q.
Tips for SBI PO
- Read carefully – note whether the percent refers to increase, decrease, of, etc.
- Write equations – keep the “%” symbol out of the arithmetic until the last step.
- Check units – always end with “₹” or “%” as appropriate.
- Practice – mix problems involving percent of a number, percent change, and ratio‑percent conversions.