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?

Correct Option (1)

To determine the time required to complete 40% of the work when X and Y work together, first calculate the individual time each person takes to complete the entire work.

• Person X completes 20% of the work in 8 days. Therefore, X completes 100% of the work in $8\times \frac{100}{20}=8\times 5=40$ days.
• Person Y completes 25% of the work in 6 days. Therefore, Y completes 100% of the work in $6\times \frac{100}{25}=6\times 4=24$ days.

Next, calculate the time taken for X and Y to complete 100% of the work together. Using the formula for combined work rate:

Combined time $=\frac{{\text{Time}}_X\times {\text{Time}}_Y}{{\text{Time}}_X+{\text{Time}}_Y}=\frac{40\times 24}{40+24}=\frac{960}{64}=15$ days.

Finally, calculate the time required to complete 40% of the work:

Time for 40% work $=\frac{40}{100}\times 15=0.4\times 15=6$ days.

Incorrect Options:

Options 2, 3, and 4 are incorrect as the calculated time for completing 40% of the work when X and Y work together is 6 days, which corresponds to Option 1.