Time and Work Questions for AFCAT

Core Concept: Work as a Rate

Think of work as filling a bucket. If A fills it in 10 days, then in 1 day A fills 1/10th of the bucket. This fraction is called the work rate or efficiency. The golden rule is: Work Done = Rate x Time. All Time and Work problems reduce to combining or comparing these rates.

• If a person completes a job in N days, their 1-day work = 1/N
• Total work is always assumed = 1 (the whole job)
• Combined rate of A and B together = 1/A + 1/B
• Time taken together = 1 divided by combined rate
• If work is given in units (not fraction), scale proportionally

LCM Method (Faster for AFCAT)

Instead of working with fractions, assume total work = LCM of all given days. Then each person's efficiency becomes a whole number. This method is faster and less error-prone in exam conditions. Think of it as counting bricks instead of fractions of a wall.

• Step 1: Find LCM of all days given in the problem
• Step 2: Efficiency of each person = LCM divided by their individual days
• Step 3: Combined efficiency = sum of individual efficiencies
• Step 4: Days to complete = Total Work (LCM) divided by combined efficiency
• This method avoids messy fractions completely

Midway / Alternate Work Problems

AFCAT frequently asks: A works for some days, then B joins (or A leaves). You need to find total time. Strategy: Calculate work done in the first phase, find remaining work, then apply the new rate for the second phase. For alternate day problems, calculate work done in a 2-day cycle and multiply.

• Midway join: Work done before joining + Work done together = 1
• For alternate days: Find work in 1 cycle (e.g., 2 days), then multiply cycles
• Always check if remaining work finishes in full days or partial days
• If A leaves early, remaining work is done by B alone — set up equation clearly
• LCM method makes midway problems much cleaner

Pipes and Cisterns

This is just Time and Work in disguise. Inlet pipes fill the tank (positive rate), outlet pipes or leaks drain it (negative rate). Treat filling as positive efficiency and draining as negative. Everything else is identical to standard work problems.

• Inlet pipe fills in A hours — rate = +1/A
• Outlet pipe empties in B hours — rate = -1/B
• Net rate = sum of all positive rates minus all negative rates
• Time to fill = 1 divided by net rate
• If net rate is negative, tank will never fill — it empties instead

• Adding days directly instead of adding rates: A takes 10 days + B takes 20 days does NOT mean together they take 30 days. Always add 1/10 + 1/20, never 10 + 20.
• Forgetting to check if the answer is a fraction of a day: AFCAT options sometimes give hours or mixed numbers — convert 0.5 days to 12 hours if needed.
• In pipes and cisterns, treating outlet as positive rate: Always subtract outlet/leak rate from inlet rate or you get a wrong sign and wrong answer.
• Using the two-person formula T = AB/(A+B) for three or more people: This formula works only for exactly two workers. For three, use the LCM method.
• In alternate-day problems, assuming both work every day: If A works on odd days and B on even days, calculate a 2-day cycle first, do not just add their rates directly.

• RATE FIRST, DAYS LAST: Always convert days to rates (1/N) before doing any math. Never touch days directly in addition or subtraction.
• LCM = Your Best Friend: Whenever you see multiple workers, immediately find LCM and convert to efficiency units. It turns fractions into whole numbers instantly.
• FILL PLUS, DRAIN MINUS: For pipes, write all inlets as positive (+) and all outlets as negative (-). Add them up. Done.
• The Bucket Analogy: Each worker fills a fraction of the bucket per day. Adding workers = adding bucket-fill speeds. If one pokes a hole (leak), subtract that speed.

• AFCAT typically has 2-3 Time and Work questions per paper. At least one will be a straightforward two-person combined work problem — free marks if you know the formula.
• One question is usually a midway variation — A works alone for X days then B joins. Use LCM method here to avoid fraction errors under time pressure.
• Pipes and Cisterns appears in roughly 40-50 percent of papers as a substitute question in place of a standard work problem. Treat it identically — same method.
• Answer options in AFCAT are usually clean numbers or simple fractions. If your calculation gives a messy decimal, you have likely made a sign error or added days instead of rates.
• Target under 75 seconds per question. If it crosses 90 seconds, mark and move on. The LCM method should keep you well within time on standard questions.