SBI Clerk /Quantitative Aptitude

Ratio & proportion

Arithmetic · free study notes

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📚 Ratio & Proportion – Study Notes

(For SBI Clerk – Quantitative Aptitude)

1. What is a Ratio?

  • A ratio compares two numbers.
  • Think of it like comparing two piles of apples.
    • If one pile has 4 apples and the other 6, the ratio is 4 : 6 (read “four to six”).
  • Ratios can be written with a colon : or a slash /.

Tiny Example
Pile A = 3 apples, Pile B = 9 apples → Ratio = 3 : 9 → simplifies to 1 : 3.

2. What is a Proportion?

  • Two ratios are in proportion when they’re equal.
  • It’s like saying “the same rate”.
  • Example:
    • 2 : 3 is in proportion to 4 : 6 because 2/3 = 4/6.

Everyday Analogy
Imagine two recipes that use the same ingredient amounts.
If one recipe calls for 2 cups of flour per 3 cups of sugar, and another calls for 4 cups flour per 6 cups sugar, they’re proportional—just scaled up.

3. Why Do We Need Proportion?

  • To find a missing part when two things grow in the same ratio.
  • Common in SBI questions:
    • “If 5 pens cost ₹25, how many pens cost ₹50?”
    • “If 3 people finish a job in 6 hours, how long will 6 people take?”

4. Basic Rule – Cross Multiplication

  • For a proportion a : b = c : d, cross‑multiply: 
    a × d  =  b × c
  • If you know three values, you can solve for the fourth.

Tiny Example
4 : 5 = x : 10
Cross‑multiply → 4 × 10 = 5 × x → 40 = 5x → x = 8.

5. Step‑by‑Step Method (SBI‑Friendly)

Step Action Quick Tip
1 Identify the two ratios (or one ratio with a missing part). Look for “is to” or “equals” in the sentence.
2 If missing part is in denominator, remember to flip. “Missing in the middle” → treat as a variable.
3 Write the proportion in cross‑multiplication form. a/b = c/d → a*d = b*c.
4 Solve for the unknown (multiply/divide). Keep numbers simple; factor out common multiples first.
5 Check the answer by substituting back. Does the original ratio hold?

6. Quick Tricks for SBI Questions

Situation Trick
Same ratio, scaled up Multiply both sides by the same number.
Inverse ratio Swap the numbers; e.g., if x : y = 1 : 4, then y : x = 4 : 1.
Finding a part of a whole Use “part in proportion to whole” → part = (whole × desired ratio part) ÷ total ratio parts.
Time–work problems Treat “work” as a common whole.
Cost problems Treat “cost” as directly proportional to “quantity”.

7. Quick Practice Problems

  1. Cost Problem

    • If 6 pencils cost ₹12, how many pencils cost ₹20?

  2. Work Problem

    • 4 workers finish a task in 10 days. How many days will 8 workers take?

  3. Recipe Scaling

    • A recipe that serves 4 uses 2 cups of flour. How many cups for 10 servings?

  4. Proportion Check

    • Is 3 : 5 proportional to 9 : 15?

  5. Missing Part

    • 7 : 9 = 21 : x → find x.

8. Quick Solutions

  1. 6 pencils : ₹12 = x pencils : ₹20

    • Cross: 6 × 20 = 12 × x → 120 = 12x → x = 10.
    • Answer: 10 pencils.

  2. 4 workers : 10 days = 8 workers : x days

    • Cross: 4 × x = 10 × 8 → 4x = 80 → x = 20.
    • Answer: 20 days.

  3. 4 servings : 2 cups = 10 servings : x cups

    • Cross: 4 × x = 2 × 10 → 4x = 20 → x = 5.
    • Answer: 5 cups.

  4. 3 : 5 = 9 : 15

    • Cross: 3 × 15 = 5 × 9 → 45 = 45 → Yes, they are proportional.

  5. 7 : 9 = 21 : x

    • Cross: 7 × x = 9 × 21 → 7x = 189 → x = 27.
    • Answer: 27.

9. Summary

  • Ratio = comparison of two numbers.
  • Proportion = two ratios that are equal.
  • Use cross multiplication to find missing parts.
  • Apply the steps carefully; double‑check with a quick substitution.

With these basics,

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