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Work and Efficiency Based Data Sufficiency

Introduction

Work and Efficiency based Data Sufficiency problems test whether the information provided is enough to determine the time, rate, or capacity of workers, machines, or pipes. These questions combine arithmetic work concepts with logical sufficiency - you must decide if the given statements independently or jointly provide enough data to answer the question.

This pattern is crucial because it connects real-world rate problems (like work-time or pipe-fill situations) with logical evaluation - an essential reasoning skill in competitive exams.

Pattern: Work and Efficiency Based Data Sufficiency

Pattern

The key formula is: Work = Rate × Time.

Each statement provides either work, rate, or time. You must check whether one or both statements together can determine the unknown (e.g., total time, combined rate, or efficiency ratio).

Step-by-Step Example

Question

How long will A take to finish the work alone?
(I) A and B together can finish the work in 6 days.
(II) B is twice as fast as A.

Choose the correct option:
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 = 1/6 work per day. But individual rates unknown → (I) alone insufficient.

  2. Step 2: Analyze Statement (II)

    B = 2A (efficiency ratio known), but no total time or combined rate → (II) alone insufficient.

  3. Step 3: Combine Statements

    From (I): A + B = 1/6 → A + 2A = 1/6 → 3A = 1/6 → A = 1/18. Hence, A alone can finish the work in 18 days.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    (I) + (II) together provide both relation and total rate ✅

Quick Variations

1. Individual work-time vs combined work-time questions.

2. Efficiency ratio between two workers (A : B).

3. Pipes & Cisterns problems framed in sufficiency format.

4. Comparative efficiency problems with days taken.

5. Work-done fraction based sufficiency (like “A does half the work in 9 days”).

Trick to Always Use

  • Step 1: Translate all data into the form Work = Rate × Time or Daily Work = 1/Days.
  • Step 2: Check if a statement gives both rate and time or their ratio.
  • Step 3: Combine statements only if one gives relationship and the other gives total rate/time.
  • Step 4: Do not calculate actual work; just check sufficiency.

Summary

Summary

  • Convert all statements into rate (work per day) form before testing sufficiency.
  • One statement is sufficient if it provides complete rate or total time data.
  • If one gives a relation (like B = 2A) and another gives a combined time, both are necessary.
  • Always test each statement independently before combining.

Example to remember:
(I) A + B = 1/6; (II) B = 2A → A = 1/18 → Both statements together are necessary.

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.

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