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Work and Efficiency Based Data Sufficiency

Introduction

Work and Efficiency आधारित Data Sufficiency problems यह जांचते हैं कि दिया गया information किसी worker, machine, या pipe की time, rate, या capacity को पता करने के लिए पर्याप्त है या नहीं। ये questions arithmetic work concepts और logical sufficiency को मिलाते हैं - आपको यह तय करना होता है कि दिए गए statements independently या jointly प्रश्न का उत्तर देने के लिए पर्याप्त हैं या नहीं।

यह pattern महत्वपूर्ण है क्योंकि यह real-world rate problems (जैसे work-time या pipe-fill situations) को logical evaluation से जोड़ता है - जो competitive exams में एक आवश्यक reasoning skill है।

Pattern: Work and Efficiency Based Data Sufficiency

Pattern

मुख्य सूत्र: Work = Rate × Time.

हर statement या तो work, rate, या time देता है। आपको जांचना है कि कौन-सा statement या दोनों मिलकर unknown (जैसे total time, combined rate, या efficiency ratio) को निश्चित रूप से determine कर पाते हैं।

Step-by-Step Example

Question

A अकेला काम पूरा करने में कितना समय लेगा?
(I) A और B साथ मिलकर काम 6 दिनों में कर लेते हैं।
(II) B, A से दो गुना तेज़ है।

सही विकल्प चुनें:
A. केवल (I) पर्याप्त है
B. केवल (II) पर्याप्त है
C. प्रत्येक statement अकेला पर्याप्त है
D. दोनों statements साथ में आवश्यक हैं

Solution

  1. Step 1: Statement (I) analyze करें

    A + B = 1/6 work per day. पर individual rates ज्ञात नहीं → (I) अकेला insufficient है।

  2. Step 2: Statement (II) analyze करें

    B = 2A (efficiency ratio पता है), पर कुल समय या combined rate नहीं दिया → (II) अकेला insufficient है।

  3. Step 3: Statements combine करें

    (I) से: A + B = 1/6 → A + 2A = 1/6 → 3A = 1/6 → A = 1/18. इसलिए A अकेला काम 18 दिन में पूरा कर सकता है।

  4. Final Answer:

    दोनों statements साथ में आवश्यक हैं → Option D

  5. Quick Check:

    (I) + (II) मिलकर relation और total rate दोनों देते हैं ✅

Quick Variations

1. Individual work-time और combined work-time वाले प्रश्न।

2. दो workers के बीच efficiency ratio (A : B)।

3. Pipes & Cisterns वाले problems जिन्हें sufficiency format में दिया गया हो।

4. Comparative efficiency प्रश्न जहाँ दिए गए अलग-अलग days होते हैं।

5. Work-done fraction आधारित sufficiency (जैसे “A आधा काम 9 दिनों में करता है”)।

Trick to Always Use

  • Step 1: सभी data को Work = Rate × Time या daily work = 1/Days के रूप में लिखें।
  • Step 2: देखें कि क्या कोई statement rate और time या उनका ratio देता है।
  • Step 3: केवल तभी combine करें जब एक statement relation देता है और दूसरा combined rate/time देता हो।
  • Step 4: actual work calculate करने की कोशिश न करें; सिर्फ sufficiency चेक करें।

Summary

Summary

  • सभी statements को rate (work per day) form में convert करके sufficiency जांचें।
  • किसी statement को तभी sufficient मानें जब वह complete rate या total time का डेटा दे।
  • अगर एक statement relation (जैसे B = 2A) देता है और दूसरा combined time देता है, तो दोनों साथ में आवश्यक होते हैं।
  • हर statement को पहले independently test करें, फिर आवश्यकता होने पर combine करें।

याद रखने वाला Example:
(I) A + B = 1/6; (II) B = 2A → A = 1/18 → दोनों statements साथ में आवश्यक हैं।

Practice

(1/5)
1. How long will A alone take to complete the work?<br>(I) A alone can complete the work in 10 days.<br>(II) A and B together can complete the work in 6 days.
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 Statement (I)

    (I) states A = 1/10 work per day ⇒ directly gives A’s time → (I) alone is sufficient.

  2. Step 2: Analyze Statement (II)

    (II) gives A + B = 1/6 per day → without B’s rate, (II) alone is insufficient to find A’s individual time.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    (I) gives A = 10 days directly; (II) does not → correct ✅
Hint: If a statement gives the individual's time directly, it is sufficient for that individual's time.
Common Mistakes: Trying to derive individual time from combined rate without any individual data.
2. In how many days can C alone finish the work?<br>(I) A is twice as fast as C.<br>(II) C alone takes 18 days.
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 Statement (I)

    (I) gives a relation A = 2C (efficiency ratio) but provides no numeric time → insufficient alone to get C’s time.

  2. Step 2: Analyze Statement (II)

    (II) states C = 18 days directly → (II) alone is sufficient to answer the question.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    Statement (II) directly gives C’s time = 18 days ✅
Hint: A direct numeric for the asked worker is sufficient even if relations exist elsewhere.
Common Mistakes: Confusing a relation (ratio) with an actual numeric value for the target worker.
3. How many days will B alone take to finish the work?<br>(I) B completes half the work in 6 days.<br>(II) B can complete the entire work in 12 days.
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 Statement (I)

    If B does half the work in 6 days ⇒ full work in 12 days ⇒ (I) alone is sufficient.

  2. Step 2: Analyze Statement (II)

    (II) directly states B = 12 days ⇒ (II) alone is also sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both (I) and (II) independently give B = 12 days ✅
Hint: If a statement gives time for a fraction of work, scale it to get full time.
Common Mistakes: Missing that 'half the work in x' directly implies full work in 2x.
4. How long will A and B together take to finish the job?<br>(I) A and B together can finish the job in 6 days.<br>(II) B alone can finish the job in 18 days, and A is twice as efficient as B.
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 Statement (I)

    (I) directly gives the combined time = 6 days → sufficient alone.

  2. Step 2: Analyze Statement (II)

    (II) gives B = 18 days and A = twice as efficient ⇒ A = 9 days. Combined rate = 1/9 + 1/18 = 1/6 → combined time = 6 days → sufficient alone.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both statements independently yield total time = 6 days ✅
Hint: If one statement directly gives the total time, or a ratio + single worker’s time gives the same, both are sufficient independently.
Common Mistakes: Believing the ratio statement always needs to be combined when it already gives enough data with one worker’s time.
5. How long will pipe A take to fill the tank?<br>(I) Pipe A and B together fill the tank in 5 hours.<br>(II) Pipe B alone fills the tank in 10 hours.
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 Statement (I)

    (A + B) = 1/5 per hour → insufficient alone to find A.

  2. Step 2: Analyze Statement (II)

    B = 1/10 per hour → insufficient alone to find A.

  3. Step 3: Combine

    A = 1/5 - 1/10 = 1/10 ⇒ A alone fills the tank in 10 hours → both together necessary.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    A+B=1/5; B=1/10 ⇒ A=1/10 ⇒ 10 hours ✅
Hint: Subtract known individual rate from combined rate to get the other.
Common Mistakes: Trying to deduce A from combined rate without individual rate.

Mock Test

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