Question

A can complete a work in 30 days and B can complete the same work in 20 days. If A and B work together, the number of days required for them to complete the work is

• A. 25 days
• B. 12 days
• C. 15 days
• D. 16 days

Answer 1

The Correct Option is B

The rate of work for A is \( \frac{1}{30} \) per day and for B is \( \frac{1}{20} \) per day. Together, their combined rate of work is: \[ \frac{1}{30} + \frac{1}{20} = \frac{2}{60} + \frac{3}{60} = \frac{5}{60} = \frac{1}{12} \] The time taken to complete the work is the reciprocal of the combined rate, i.e., 12 days. 
When two people work together, add their individual work rates to find the combined rate. The time taken is the reciprocal of the combined rate.