Time & Work — Together We Finish Faster
✨ IN SHORT — THE WHOLE LESSON IN 20 SECONDS
Think in 'work per day'. If A finishes in 10 days, A does 1/10 of the job daily. Add the daily parts of everyone working together — that's the whole chapter.
1. Daily Work Method
A in 12 days → 1/12 per day. B in 15 days → 1/15 per day. Together: 1/12 + 1/15 = 9/60 = 3/20 per day → finish in 20/3 ≈ 6.67 days.
📌 Shortcut for two workers: days together = (a×b)/(a+b). 12 & 15 → 180/27 = 6.67 days.
2. LCM Method (student favourite)
Take total work = LCM of days. A 10 days, B 15 days → total 30 units. A does 3/day, B does 2/day. Together 5/day → 30/5 = 6 days. No fractions, no fear.
💡 Trick: LCM method keeps every number whole. Use it whenever days are given.
3. Man-Days Rule (M1D1 = M2D2)
Men × Days stays constant for the same job. 10 men finish in 20 days → 200 man-days. 25 men need 200/25 = 8 days. If hours/day change too: M1×D1×H1 = M2×D2×H2.
📌 5 men, 12 days → 60 man-days. 6 men → 60/6 = 10 days.
⚡ Now Practise — 8 Questions
Tap an answer. Right or wrong, we explain why instantly. Learn from every tap!
Q1. A alone finishes work in 20 days. A's one-day work is:
Q2. A in 10 days, B in 15 days. Together they finish in:
Q3. 12 men complete a job in 15 days. 20 men will take:
Q4. A and B together finish in 12 days. A alone in 20 days. B alone takes:
Q5. If 6 workers build a wall in 10 days working 8 hrs/day, total work-hours needed:
Q6. A does a job in 25 days. In 5 days, fraction done is:
Q7. Two pipes fill a tank in 6 and 12 hours. Together:
Q8. 8 men or 12 women finish a job in 20 days. Man-days equivalent total:
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