Ram can do a piece of work in 10 days and Anshu in 20 days. They work together, but 2 days before the completion of the work, Ram leaves and Anshu completes the work. In total how many days was the work completed?

8 days

The correct answer is Option (3) → 8 days

1. Find Total Work and Daily Efficiency

Let's find the Least Common Multiple (LCM) of the days taken by Ram and Anshu to define the "Total Work Units."

• Ram: 10 days
• Anshu: 20 days
• Total Work (LCM of 10 and 20): 20 units

Now, calculate their daily work (efficiency):

• Ram's Efficiency: $20 \div 10 = 2 \text{ units/day}$
• Anshu's Efficiency: $20 \div 20 = 1 \text{ unit/day}$
• Combined Efficiency: $2 + 1 = 3 \text{ units/day}$

2. Analyze the Last 2 Days

The problem states that Ram leaves 2 days before completion. This means for the final 2 days, only Anshu was working.

• Work done by Anshu in the last 2 days: $1 \text{ unit/day} \times 2 \text{ days} = 2 \text{ units}$.

3. Analyze the Work Done Together

If 2 units were done at the very end, the remaining work must have been done by Ram and Anshu working together.

• Remaining work: $20 - 2 = 18 \text{ units}$.
• Time spent working together: $\frac{18 \text{ units}}{3 \text{ units/day}} = 6 \text{ days}$.

4. Total Time

To find the total duration, add the "together" phase and the "Anshu alone" phase:

$\text{Total Days} = 6 \text{ days (together)} + 2 \text{ days (Anshu alone)} = 8 \text{ days}$