Arun takes twice as much time as Mradul and thrice as much as Chaman to complete a piece of work. They together complete the work in 1 day. In what time will Arun alone complete the work?

Let Chaman's time alone be x days. Then Arun takes 3x days and Mradul takes x/2 days. Their rates: Arun = 1/3x, Mradul = 2/x, Chaman = 1/x. Combined rate: 1/3x + 2/x + 1/x = (1+6+3)/3x = 10/3x = 1 (since they complete in 1 day). Thus 3x = 10, so x = 10/3. Arun's time = 3x = 3(10/3) = 10 days? Wait, re-reading: Arun = 2 × Mradul's time means Arun takes longer. Let Arun = 2M, Arun = 3C, and 1/A + 1/M + 1/C = 1. Substituting: 1/(2M) + 1/M + 1/(M/3) = 1/2M + 1/M + 3/M = 4.5/M = 1, so M = 4.5. Then Arun = 2(4.5) = 9? Hmm, but answer is 6. Let me reconsider: 'Arun takes twice as much as Mradul' means A = 2M. 'Thrice as much as Chaman' means A = 3C, so C = A/3. Together: 1/A + 1/(A/2) + 1/(A/3) = 1/A + 2/A + 3/A = 6/A = 1, so A = 6 days.