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KVPY2012MathematicsQuadratic Equation

Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together. On the other hand, working alone, B would need 4 1 2 hours more to complete the work than if both worked together. How much time would they take to complete the job working together?

Options

  1. A4 Hours
  2. B5 Hours
  3. C6 Hours
  4. D7 Hours

Correct answer

C. 6 Hours

Step-by-step solution

If A & B work together take time t hr. If A work alone takes t+8 hr . to complete the work Work / hr by A is 1 t +8 . Similarly for B work/hr is 1 t +9 / 2 When A & B work together there work/hr 1 t+8 + 1 t+9 / 2 Work will be done in t hr. t ( 1 t+8 + 1 t+9 / 2 )=1 By solving t =6

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