SSC CGL Preparation – Day 7

Quantitative Aptitude – Time and Work

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1. Basic Concepts

• Work: Any task to be completed.
• Unitary Method: If A can complete work in x days, then A’s 1 day work = 1/x.

🧠 Example:

If A can do a job in 5 days, A’s 1-day work = 1/5.

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2. Important Formulas

Situation	Formula
Work = Time × Rate of work	Work = Days × (1/Days per person)
If A can do a work in x days, B in y days	Then both in 1 day = (1/x + 1/y)
If A is ‘n’ times efficient than B	A takes 1/n of the time B takes

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3. Combined Work

If A can do a work in x days and B in y days, together they will do:

• 1 day work = 1/x + 1/y
• Total time = xy / (x + y)

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4. Work and Wages

If A and B work together and complete a work and their efficiencies are known, then:

• Wages are divided in the ratio of work done (or efficiency × time worked).

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5. Pipes and Cisterns

(Pipes filling or emptying tanks – same logic as Time and Work)

• If pipe A fills tank in x hrs, 1 hour work = 1/x
• If pipe B empties tank in y hrs, 1 hour work = -1/y
• Net work per hour = (1/x – 1/y)

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6. Alternate Days Work

If A and B work on alternate days, calculate their total work per 2 days and then determine how many such pairs fit into total work.

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7. Efficiency-Based Problems

If A is twice as efficient as B, then:

• A’s work per day = 2 units (say), B’s = 1 unit
• Total work can be considered in efficiency units.

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🧮 Common Shortcuts

• Work = LCM of individual days (assume total work as LCM)
• Use ratio method to assign work and time
• Efficiency = 1/Time taken

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🧑‍🏫 Examples

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Example 1:
A can do a piece of work in 10 days, B in 15 days. Working together, how long will they take?

Solution:
A’s 1-day work = 1/10, B’s = 1/15
Combined 1-day work = (1/10 + 1/15) = (3+2)/30 = 5/30 = 1/6
⇒ Time = 6 days

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Example 2:
A is twice as efficient as B. Together they can complete a work in 12 days. How many days will A take alone?

Solution:
Let B’s 1-day work = x, so A = 2x
Combined = x + 2x = 3x
3x × 12 = 1 → x = 1/36
A’s 1-day work = 2/36 = 1/18
So, A alone can do the work in 18 days

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Example 3:
Two pipes A and B can fill a tank in 20 min and 30 min respectively. Pipe C can empty it in 15 min. If all three are opened together, in how much time will the tank be filled?

Solution:
A’s work = 1/20, B’s = 1/30, C’s = -1/15
Net = 1/20 + 1/30 – 1/15
= (3 + 2 – 4)/60 = 1/60
⇒ Tank filled in 60 min

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📝 Tips for SSC CGL

Practice Pipes & Cisterns as they are just inverse work problems.

Expect 2–3 questions from this topic.

Be quick with LCM-based methods.

Understand efficiency problems deeply.