A can do a piece of work in 20 days and B can do it in 30 days. In how many days can A and B together finish the work?

English বাংলা

Answer

12 days

Explanation

A's one day work is \( \frac{1}{20} \), B's one day work is \( \frac{1}{30} \). Combined one day work is \( \frac{1}{20} + \frac{1}{30} = \frac{3+2}{60} = \frac{5}{60} = \frac{1}{12} \). Thus, they will finish the work together in 12 days.

Key Points

  • > Combined time \( = \frac{xy}{x+y} \)
  • > Here \( x = 20 \) and \( y = 30 \)
  • > Time and work capacity are inversely proportional

Additional Information

  • It is often easier to assume the total work as the Least Common Multiple (LCM).
  • LCM of \( 20, 30 = 60 \) units.
  • A's efficiency = 3 units/day, B's efficiency = 2 units/day.
MethodExplanation
LCM MethodDivide total work by efficiency
Fraction MethodAdd daily work rates
Mathematics Time and Work Medium

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