Time & Work

Mathematics · 6 min read · Sunitha Rao

Work rates, combined work and the efficiency method.

Treat work as a quantity and speed as work per day. If A finishes a job in 10 days, A's one-day work is 1/10. Adding rates is what makes combined-work questions easy: A and B together do 1/10 + 1/15 = 1/6 of the job daily, so they take 6 days.

The LCM method is faster than fractions. For 10 and 15 days, assume the total work is 30 units; then A does 3 units a day and B does 2, giving 5 units a day together and 30/5 = 6 days.

Efficiency questions follow the same logic in reverse: if A is twice as efficient as B, A takes half the time B does.

Important points

  • One day's work = 1 / (days taken).
  • Rates add when people work together; they subtract when one empties a tank.
  • Use LCM of the given days as total work to avoid fractions.
  • Efficiency and time taken are inversely proportional.

Key formulas

Together time = (a x b) / (a + b)

Work = Rate x Time

Examples

  1. A takes 10 days, B takes 15 days. Together = 1/10 + 1/15 = 1/6, so 6 days.
  2. A pipe fills a tank in 6 hours, a leak empties it in 12. Net = 1/6 - 1/12 = 1/12, so 12 hours.

Practise Time & Work questions →