Question

The ratio of the time taken by A and B to complete a task is 3: 2. If B can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?

• A. 12 hrs
• B. 10.8 hrs
• C. 9.8 hrs
• D. 9 hrs

Answer 1

Answer:

B. 10.8 hrs

Given:

• Time ratio (A:B = 3:2)

• (B) alone takes 18 hours

Step 1: Find A’s time

Since (B) corresponds to 2 parts:

$2 \text{ parts} = 18 \Rightarrow 1 \text{ part} = 9$

So,
$A = 3 \text{ parts} = 3 \times 9 = 27 \text{ hours}$

Step 2: Work rates

• A’s 1-hour work =$( \frac{1}{27} )$

• B’s 1-hour work = $( \frac{1}{18} )$

Together:

$\frac{1}{27} + \frac{1}{18}$
$= \frac{2 + 3}{54}$
$= \frac{5}{54}$

Step 3: Time together

$\text{Time} = \frac{1}{5/54} = \frac{54}{5} = 10.8 \text{ hours}$