Question

Baban takes 8 hours to do a job. Mahendra takes 10 hours to do the same job. How long should it take both Baban and Mahendra, working together but independently, to do the same job?

• A. \( \frac{40}{11} \)
• B. \( \frac{40}{9} \)
• C. \( \frac{9}{40} \)
• D. 9
• E.

Hint:

When two people work together, their combined work rate is the sum of their individual rates. Use the formula: \[ \text{Time taken together} = \frac{1}{\text{Combined work rate}}. \]

Answer 1

The Correct Option is B

Step 1: Calculate the work done by each person in 1 hour. - Work done by Baban in 1 hour: \[ \frac{1}{8} \] - Work done by Mahendra in 1 hour: \[ \frac{1}{10} \] Step 2: Determine their combined work per hour: \[ \frac{1}{8} + \frac{1}{10} = \frac{5}{40} + \frac{4}{40} = \frac{9}{40}. \] Step 3: Calculate the total time required to complete the work when working together: \[ \text{Time} = \frac{1}{\frac{9}{40}} = \frac{40}{9}. \] Thus, the total time required for Baban and Mahendra to complete the job together is \( \frac{40}{9} \) hours.