Q. 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?

Explanation :

Let’s solve how long it takes two people to complete 40% of work together.

Given:
Person 1:
– Can do 20% (W/5) of work in 8 days
– Rate = (W/5)/8 = W/40 per day

Person 2:
– Can do 25% (W/4) of work in 6 days
– Rate = (W/4)/6 = W/24 per day

Step by step calculations:
1. Combined rate of work = Rate of Person 1 + Rate of Person 2
= W/40 + W/24
= (24W + 40W)/(40 × 24)
= 64W/960
= W/15 per day

2. Time to complete 40% work:
Work = Rate × Time
0.4W = (W/15) × Time
Time = (0.4W) ÷ (W/15)
= 0.4W × (15/W)
= 0.4 × 15
= 6 days

Therefore, working together, they will complete 40% of the work in 6 days.