Question

A can do a work in 10 days and B can do the same work in 15 days. Both together can do the same work in

• A. 4 days
• B. 5 days
• C. 6 days
• D. 8 days

Hint:

When two people work together, add their work rates. Then take the reciprocal to find total time to finish the work.

Answer 1

The Correct Option is C

Let total work = 1 unit (we assume 1 full job to be done) Step 1: Work done by A in 1 day = \( \frac{1}{10} \)
Work done by B in 1 day = \( \frac{1}{15} \) Step 2: Total work done together in 1 day
\[ \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6} \] Step 3: Total time to finish 1 job together
\[ \text{Time} = \frac{1}{\frac{1}{6}} = \boxed{6 \text{ days}} \]