Question

'A' can complete a task in 10 days whereas 'B' can complete the same task in 15 days. If 'A' and 'B' work on alternate days starting with 'A', then what is the total number of days required to complete the task?

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

The Correct Option is B

Step 1: Define Work Rates

The total work is equivalent to completing 1 full task. The rates at which A and B work are:

\[ A = \frac{1}{10}, \quad B = \frac{1}{15} \] 

Step 2: Work Done in Two Days

Since A and B work on alternate days, their combined work in two days is:

\[ \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \]

Step 3: Calculate Total Days

In 12 days (which includes 6 cycles of 2 days), they complete:

\[ 6 \times \frac{1}{6} = 1 \]

Final Conclusion:

The total number of days required to complete the work is 12.

Correct answer: (B) 12.