A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

The correct option is 6 (or 6 days).

Let's solve the problem step-by-step to find the total time required for X and Y working together to complete 40% of the work.

Step 1: Calculate the time taken by X and Y to complete 100% of the work individually.

Person X completes 20% of the work in 8 days.
Since 20% is equal to $\frac{1}{5}$ of the work, X will take:
$8\times 5=40$ days to complete 100% of the work.

Person Y completes 25% of the work in 6 days.
Since 25% is equal to $\frac{1}{4}$ of the work, Y will take:
$6\times 4=24$ days to complete 100% of the work.

Step 2: Find the 1-day work of X and Y working together.

Work done by X in 1 day = $\frac{1}{40}$

Work done by Y in 1 day = $\frac{1}{24}$

Combined work done by X and Y in 1 day:
$\frac{1}{40}+\frac{1}{24}$

Taking the Least Common Multiple (LCM) of 40 and 24, which is 120:
$\frac{3+5}{120}=\frac{8}{120}=\frac{1}{15}$

Thus, together X and Y can complete $\frac{1}{15}$ of the work in 1 day (or the entire 100% work in 15 days).

Step 3: Calculate the time taken to complete 40% of the work.

40% of the work corresponds to:
$\frac{40}{100}=\frac{2}{5}$ of the total work.

Number of days required to complete $\frac{2}{5}$ of the work:
$\text{Days}=\frac{2/5}{1/15}=\frac{2}{5}\times 15=2\times 3=6$ days.

Hence, working together, X and Y will complete 40% of the work in 6 days.