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Ratio / Percentage Based Sufficiency

Introduction

Ratio and percentage problems often hide the relation between two or more quantities. In Data Sufficiency style questions you must decide whether the statements given provide enough information to determine a ratio or percentage-related value - not necessarily to compute every number.

This pattern is important because percentages and ratios are everywhere in exams and real life (salary changes, profit margins, population shares). Learning to judge sufficiency quickly saves time and prevents unnecessary calculation.

Pattern: Ratio / Percentage Based Sufficiency

Pattern

Key idea - Translate percentage statements into multiplicative relations and ratios; check whether those relations uniquely determine the required ratio or percentage.

Typical stems ask for a ratio (A : B) or a percentage change. Statements may give direct ratios, percentage increases/decreases, or totals/parts. Your task: test each statement separately for uniqueness, then together if needed.

Step-by-Step Example

Question

What is the ratio of A : B?
(I) A is 20% more than B.
(II) A + B = ₹1,20,000

Solution

  1. Step 1: Translate Statement (I)

    “A is 20% more than B” means A = B + 0.20·B = 1.20·B. So A : B = 1.20 : 1 → multiplying by 100 gives 120 : 100 → simplify → 6 : 5. Thus (I) alone gives a unique ratio.

  2. Step 2: Analyze Statement (II)

    (II) gives the total A + B = ₹1,20,000 but does not give the relation between A and B. Without a relation, many pairs (A, B) can sum to ₹1,20,000 (for example, 60,000 & 60,000; 70,000 & 50,000; etc.). Therefore (II) alone is insufficient to determine A : B.

  3. Step 3: Compare Sufficiency

    Since (I) alone yields A : B = 6 : 5, it is sufficient by itself. (II) is insufficient. Combining (I) and (II) would allow computing absolute values (A = ₹69,23,076.92... - not needed), but the ratio is already known from (I).

  4. Final Answer:

    (I) alone is sufficient; (II) alone is insufficient.

  5. Quick Check:

    From (I): A = 1.2B → A : B = 6 : 5 ✅. (II) gives many possible splits → insufficient ❌

Quick Variations

1. Percentage increase/decrease (A increased by 25%) → translate to multiplicative factor (1.25×).

2. Compound percentage statements (A increased 10% then decreased 5%) → convert stepwise into a net multiplier.

3. Mixed ratio + total: A : B given as ratio and A + B given as total → both together give absolute values; ratio alone may be sufficient for the asked ratio.

Trick to Always Use

  • Step 1 → Convert percentages to multipliers (e.g., +20% → ×1.20; -30% → ×0.70).
  • Step 2 → Express relations as ratios immediately (A = k·B → A : B = k : 1 and simplify).
  • Step 3 → If a statement gives only a total or only a part without a ratio relation, mark it insufficient alone.

Summary

Summary

  • Always convert percentage language into multiplicative factors before reasoning.
  • If a statement gives a direct multiplicative relation (A = k·B), it often determines the ratio immediately.
  • Totals (A + B) without relations are usually insufficient; combine with a ratio or percentage to get absolute values.
  • Check for uniqueness - sufficiency requires a single unambiguous ratio/value from the given statement(s).

Example to remember:
If A is 20% more than B, then A : B = 1.20 : 1 = 6 : 5 (sufficient). If only A + B = ₹1,20,000 is given, ratio is not fixed (insufficient).

Practice

(1/5)
1. What is the ratio of A’s salary to B’s salary?<br>(I) A’s salary is 25% more than B’s salary.<br>(II) The total of both salaries is ₹90,000.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    “A is 25% more than B” ⇒ A = 1.25·B ⇒ A : B = 1.25 : 1 = 5 : 4. (I) alone gives the exact ratio.

  2. Step 2: Analyze (II)

    A + B = ₹90,000 → total known, but not the relative proportion → insufficient alone.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    Convert 25% → 1.25 so ratio 5 : 4 ✅
Hint: Convert ‘more than’ % into multiplier: (1 + %/100).
Common Mistakes: Using totals without a relation between quantities.
2. By what percent is A’s income more than B’s income?<br>(I) The ratio of A’s income to B’s income is 7 : 5.<br>(II) A’s income exceeds B’s by ₹10,000.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    From (I): A : B = 7 : 5. Percentage by which A exceeds B = ((7-5)/5)×100 = (2/5)×100 = 40%. (I) alone gives the required percent.

  2. Step 2: Analyze (II)

    A - B = ₹10,000 gives the absolute difference but without the base (B) you cannot compute percent alone.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    Ratio 7:5 → (2/5) = 0.4 → 40% ✅
Hint: Percent more = (difference/base)×100; ratio gives difference and base proportionally.
Common Mistakes: Trying to compute percent from difference alone without the base value.
3. What is the ratio of marks scored by A and B?<br>(I) A scored 60% marks and B scored 40% marks in the same test.<br>(II) A scored 120 marks and B scored 80 marks in the same test.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Percentages given on same base → A : B = 60 : 40 = 3 : 2. (I) alone sufficient.

  2. Step 2: Analyze (II)

    Absolute marks 120 and 80 → A : B = 120 : 80 = 3 : 2. (II) alone also sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both (I) and (II) independently give 3 : 2 ✅
Hint: Percentages on same base or proportional absolute scores both yield the ratio directly.
Common Mistakes: Thinking totals or absolute marks are always needed when percentages suffice.
4. Find the ratio of male to female employees in a company.<br>(I) There are 300 male employees.<br>(II) Males constitute 60% of total employees.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Only male count known → total or female count missing → insufficient.

  2. Step 2: Analyze (II)

    Males are 60% of total → relation known but no actual number → insufficient alone.

  3. Step 3: Combine

    0.6·T = 300 ⇒ T = 500. Females = 200. Ratio M : F = 300 : 200 = 3 : 2. Both together are necessary.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    Combine → 300 : 200 = 3 : 2 ✅
Hint: Combine absolute counts with percentage share to compute component ratios.
Common Mistakes: Trying to infer ratio with only one type of information (count or %).
5. What is the percentage profit on an article?<br>(I) Selling price is ₹1,200.<br>(II) Profit% is 20%.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Both statements together are necessary
D. Each statement alone is sufficient

Solution

  1. Step 1: Analyze (I)

    SP = ₹1,200 alone doesn't give profit% without CP → insufficient.

  2. Step 2: Analyze (II)

    Profit% = 20% → the question asks for percentage profit, which is directly given by (II). (II) alone is sufficient.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    (II) states profit% = 20% → answer immediate ✅
Hint: If the statement directly gives the asked percentage, it is sufficient by itself.
Common Mistakes: Trying to compute profit% from SP alone without CP or % info.

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