0
0

Ratio / Percentage Based Sufficiency

Introduction

Ratio और percentage वाले problems अक्सर दो या ज़्यादा quantities के बीच relation को छिपा देते हैं। Data Sufficiency style questions में आपको यह तय करना होता है कि दिए गए statements ratio या percentage-based value तय करने के लिए पर्याप्त जानकारी देते हैं या नहीं - हर number calculate करना ज़रूरी नहीं होता।

यह pattern इसलिए महत्वपूर्ण है क्योंकि percentages और ratios exams तथा real life (salary changes, profit margins, population shares) में बहुत आम हैं। Sufficiency judge करना जल्दी सीखने से समय बचता है और अनावश्यक calculation से बचाव होता है।

Pattern: Ratio / Percentage Based Sufficiency

Pattern

मुख्य विचार - Percentage statements को multiplicative relations और ratios में translate करें; फिर check करें कि क्या वे relations required ratio या percentage को uniquely determine करते हैं।

सामान्यत: questions में A : B जैसा ratio या कोई percentage change पूछा जाता है। Statements में direct ratios, percentage increase/decrease, या totals/parts हो सकते हैं। आपका काम: हर statement को पहले अलग-अलग test करना और uniqueness देखना, फिर जरूरत पड़े तो दोनों को साथ में।

Step-by-Step Example

Question

A : B का ratio क्या है?
(I) A, B से 20% ज़्यादा है।
(II) A + B = ₹1,20,000

Solution

  1. Step 1: Statement (I) translate करें

    “A is 20% more than B” का मतलब: A = B + 0.20·B = 1.20·B। इसलिए A : B = 1.20 : 1 → 120 : 100 → simplify → 6 : 5. मतलब (I) अकेला ही unique ratio दे देता है।

  2. Step 2: Statement (II) analyze करें

    (II): A + B = ₹1,20,000 से A और B का relation नहीं मिलता। कई pairs इस total को बना सकते हैं (60k & 60k, 70k & 50k, 80k & 40k…). इसलिए (II) अकेला insufficient है।

  3. Step 3: Sufficiency compare करें

    क्योंकि (I) alone से A : B = 6 : 5 मिल जाता है, यह अपने आप sufficient है। (II) insufficient है। Combined करने पर absolute values निकल सकती हैं, पर ratio पहले ही (I) से पता है।

  4. Final Answer:

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

  5. Quick Check:

    (I): A = 1.2B → A : B = 6 : 5 ✅ (II): कई possible splits → ratio fixed नहीं ❌

Quick Variations

1. Percentage increase/decrease (A 25% बढ़ा) → multiplier form (1.25×) में बदलें।

2. Compound percentage statements (पहले 10% बढ़ा फिर 5% घटा) → stepwise multipliers में convert करें।

3. Mixed ratio + total: Ratio दिया है और A + B भी दिया है → दोनों मिलकर absolute values दे सकते हैं; ratio अकेला भी sufficient हो सकता है अगर वही पूछा है।

Trick to Always Use

  • Step 1 → Percentages को हमेशा multipliers में बदलें (+20% → ×1.20; -30% → ×0.70).
  • Step 2 → Relations को तुरंत ratios में लिखें (A = k·B → A : B = k : 1)।
  • Step 3 → अगर statement सिर्फ total या सिर्फ part दे रहा है बिना relation के, तो वह अकेला insufficient होगा।

Summary

Summary

  • Percentage language को हमेशा पहले multiplicative factor में बदलें।
  • अगर statement direct multiplicative relation देता है (A = k·B), तो ratio अक्सर तुरंत मिल जाता है।
  • Totals (A + B) बिना relation के आम तौर पर insufficient होते हैं; ratio या percentage के साथ combine करने पर ही काम करते हैं।
  • Uniqueness check करें - sufficiency तभी मानी जाएगी जब statement(s) से एक ही निश्चित ratio/value मिले।

याद रखने वाला Example:
अगर A, B से 20% ज़्यादा है → A : B = 1.20 : 1 = 6 : 5 (sufficient)। अगर सिर्फ A + B = ₹1,20,000 दिया है → ratio fixed नहीं (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.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes