A person 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?

Here's a brief explanation: 1. Calculate individual work rates: Person X completes 20% of work in 8 days. So, X completes 100% of the work in (8 / 20%) = 8 / 0.2 = 40 days. X's one-day work rate is 1/40. Person Y completes 25% of work in 6 days. So, Y completes 100% of the work in (6 / 25%) = 6 / 0.25 = 24 days. Y's one-day work rate is 1/24. 2. Calculate combined work rate: When working together, their combined one-day work rate is 1/40 + 1/24. Find a common denominator (LCM of 40 and 24 is 120): (3/120) + (5/120) = 8/120 = 1/15. This means they complete 1/15 of the work in one day. So, together they can complete 100% of the work in 15 days. 3. Calculate time for 40% of the work: To complete 40% of the work, they will take 40% of the total time required for 100% work. Time = 15 days * 40% = 15 * 0.40 = 6 days. Therefore, 40% of the work will be completed in 6 days. Analyzing the options: A) 6: This matches our calculated time. B) 8: Incorrect, this is the time X takes for 20% work. C) 10: Incorrect. D) 12: Incorrect. The final answer is A.