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…

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$8×20100​=8×5=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$6×25100​=6×4=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 $= \frac{\text{Time}_X \times \text{Time}_Y}{\text{Time}_X + \text{Time}_Y} = \frac{40 \times 24}{40 + 24} = \frac{960}{64} = 15$=TimeX​+TimeY​TimeX​×TimeY​​=40+2440×24​=64960​=15 days.

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

Time for 40% work $= \frac{40}{100} \times 15 = 0.4 \times 15 = 6$=10040​×15=0.4×15=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.