Question

A can complete a work in 12 days and B in 18 days. In how many days will they complete the work together?

• A. 6 days
• B. 7.2 days
• C. 8 days
• D. 9 days

Hint:

For two people, you can use the formula: $\text{Time} = \frac{xy}{x+y}$. In this case: $\frac{12 \times 18}{12 + 18} = \frac{216}{30} = 7.2$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When two people work together, their individual rates of work (work done per day) are added to find the combined rate. Rate is the reciprocal of the time taken.

Step 2: Identifying the Individual Rates:

• Rate of A = $\frac{1}{12}$ units/day
• Rate of B = $\frac{1}{18}$ units/day

Step 3: Calculation:
1. Combined rate: \[ \frac{1}{12} + \frac{1}{18} = \frac{3 + 2}{36} = \frac{5}{36} \] 2. Time taken together (Reciprocal of the rate): \[ \text{Time} = \frac{36}{5} = 7.2 \text{ days} \]

Step 4: Final Answer:
They will complete the work together in 7.2 days.