Rakesh starts working on a job and works on it for 6 days, completing 20% of…

Efficiency (daily work rate) is the fraction of the job completed per day: Efficiency = Work Done divided by Time Taken. When two people work together, their combined efficiency is the sum of their individual efficiencies; and 'how much more efficient A is than B' is calculated as ((Efficiency of A minus Efficiency of B) divided by Efficiency of B) times 100%.

1. Rakesh alone completes 20% of the work in 6 days, so his daily efficiency = 20% divided by 6 = 10/3 % per day.

2. After 6 days, 100% minus 20% = 80% of the work remains, and this portion is finished by Rakesh and Karan working together for 18 days.

3. Working alone at his own rate for those 18 days, Rakesh would complete 18 times 10/3 % = 60% of the work.

4. So Karan's actual share of the remaining work is 80% minus 60% = 20%, completed in 18 days, giving Karan's daily efficiency = 20 divided by 18 = 10/9 % per day.

5. Comparing the two rates: (10/3) divided by (10/9) = 3, so Rakesh's daily efficiency is 3 times Karan's.

6. How much more efficient = (3 minus 1) times 100% = 200%.

Independent check: let the total work be 90 units (a convenient common multiple). Rakesh finishes 20% of 90 = 18 units in 6 days, so his rate is 3 units per day. The remaining 72 units are finished by both in 18 days, so their combined rate is 72 divided by 18 = 4 units per day, making Karan's rate 4 minus 3 = 1 unit per day. The ratio 3:1 confirms Rakesh is 200% more efficient than Karan.