GATE CS 2010 Q64 — General Aptitude

Let the total work required to build the wall be $1$ unit.

We can find the daily work rate of a single worker in each category:

• Skilled worker ($S$):
  Since $5$ skilled workers take $20$ days, the rate of $1$ skilled worker is: $$S = \frac{1}{5 \times 20} = \frac{1}{100} \text{ of the work per day}$$
• Semi-skilled worker ($M$):
  Since $8$ semi-skilled workers take $25$ days, the rate of $1$ semi-skilled worker is: $$M = \frac{1}{8 \times 25} = \frac{1}{200} \text{ of the work per day}$$
• Unskilled worker ($U$):
  Since $10$ unskilled workers take $30$ days, the rate of $1$ unskilled worker is: $$U = \frac{1}{10 \times 30} = \frac{1}{300} \text{ of the work per day}$$

Now, we calculate the combined daily work rate ($R$) of the new team consisting of $2$ skilled, $6$ semi-skilled, and $5$ unskilled workers:

Taking the common denominator as $60$:

Therefore, the time required for this team to build the wall is:

Hence, the correct option is D.