A does half as much work as B in three-fourth of the time. If the together they take 18 days to complete a work. How much time shall B take to do it?

Radio of times taken = (1/3) : (1/4) = 4 : 3

? Mohan moves the whole lawn in x hours.
? mohan moves in 2 hours = 2/x part of the lawn.
? Unmoved part = 1 - 2/x = (x - 2)/ x part

In 25 hours A can copy 75 pages
In 1 hour A can copy 75/25 = 3 pages
In 25 hours (A and B) can copy = 135/27 = 5 pages
? In 1 hour B can copy (5 - 3) = 2 pages
? B can copy 42 pages in 21 hours.

Let C alone can finish the job in T hours.
According to the question,
Work done by A, B and C in 1h = 1/2
? 1/6 +1/5 + 1/T = 1/2
? 1/T = 1/2 - 1/6- 1/5 = (15 - 5- 6)/30
? 1/T = 4/30 = 2/15
? T = 7¹/₂ h

A 's 1 day's work = 1/4
B ' s 1 days's work = 1/12
(A+B) ' s day ' s work = 1/4 + 1/12
= (3 + 1)/12 = 4/12 = 1/3
Days required by A and B together to do the work = 1 / (A + B ) ' s day ' s work = 3 days

Work done by (A + B) in 1 day = 1/24
Work done by B alone in 1 day = 1/(3 x 12) = 1/36
? Work of A for 1 day = 1/24 - 1/36 = 1/72
After 12 days the remaining work = 1 - 1/3 = 2/3
? 1/72 work is done by A in 1 day
? 2/3 work is done by A in (1 x 72)/(1 x 2/3) = 48 days

let the work done be 1 work.
Here M1=15, D1=16 W1=W2 =1
M2 =24 D2= ?
? According to the formula
M1 D1 W2 = M2 D2 W1
? 15 x 16 x 1 = 24 x D2 X 1
? D1 = 15 X 16/24 = 10
Therefore 10 days are required to complete the work

A's 1 day's work = 1/18
B's 1 day's work = 1/9
(A + B)'s 1 day's work = 1/9 + 1/18 = 3/18 = 1/6

(A + B)'s 1 days work = 1/12
B's 1 days work = 1/30
? A's 1 days work = 1/12 - 1/30 = (5 - 2)/60 = 1/20
? A alone can finish the work in 20 days.

We have the important relation, More work, More time (days)
? A piece of work can be done in 6 days.
? Three times of work of same type can be done in 6 x 3
= 18 days