M does one-third as much work as N in one-fourth of the time. If together they take 12 days to complete a work, how much time shall N alone take to do it?

Question: M does one-third as much work as N in one-fourth of the time. If together they take 12 days to complete a work, how much time shall N alone take to do it?

Solution:
Let N takes x days to do the work.
M takes 1/4 of x time to do 1/3 of the work.
∴ The work will be done by M in (x/4) × 3 days
= 3x/4

ATQ,
1/x + 4/3x = 1/12
⇒ 7/3x = 1/12
⇒ 3x = 84
∴ x = 28

∴ N alone will take 28 days.