Question

A can complete a piece of work in 15 days and B can complete the same work in 10 days. In how many days will they complete the work together?

• A. 4 days
• B. 5 days
• C. 6 days
• D. 7 days

Hint:

The LCM method is highly effective for complex time-and-work problems.
Always try to use LCM to convert fraction-based work rates into simple whole numbers representing efficiencies.
This minimizes computational errors and speeds up the calculation process.

Answer 1

The Correct Option is C

Step 1: Use the units method.
Let the total work be the LCM of $15$ and $10$, which is $30$ units. This keeps the numbers clean.

Step 2: Find each person's daily output.
A finishes $30$ units in $15$ days, so A does $\frac{30}{15} = 2$ units a day.

Step 3: Do the same for B.
B finishes $30$ units in $10$ days, so B does $\frac{30}{10} = 3$ units a day.

Step 4: Add their daily outputs.
Together they do $2 + 3 = 5$ units each day.

Step 5: Find the time together.
Total work divided by combined rate, $\frac{30}{5} = 6$ days.

Step 6: State the answer.
Working together, they finish in $6$ days. \[ \boxed{6 \text{ days}} \]