A can build up a structure in 8 days and B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of structure?

(A + B)'s 2 day's work = (1/12) + (1/18) = 5/36
(A + B)'s 14 day's work = (5/36) x 7 = 35/36
Remaining work = 1 - (35/36) = 1/36

Now, it is the turn of A .
A's 1 day's work = 1/12
? 1/36 work is done by A in 12 x (1/36) days = 1/3 days
? Total time taken = 14¹/₃ days

Here, a₁ = 8, b₁ = 4, a₂ = 1, b₂ = 1 and n = 7
? Work done by 1 man/Work done by 1 boy = (nb₂ - b₁)/(a₁ - na₂)
= (7 x 1 - 4) / (8 - 7 x 1)
= 3

Part of field grazed by 4 goats in 1 day = 1/50
Part of field grazed by 1 goat in 1 day = (1/50) x 4 = 1/200
? 4 g = 6 s [here, g = goats, and s = sheep]
? 1 s = (4/6) g = (2/3) g
Now, 2 g + 9 s = 2 g + 9 x (2/3) g
= 2 g + 6 g = 8 g
? 8 goats can graze the field in (1/8) / 200 = 25 days

4 men = 6 women = 10 children
? 1 man = 5/2 children
1 women = 5/3 children

Now, 1 couple + 5 children = 1 man + 1 women + 5 children
= (5/2) + (5/3) + 5 = 55/6 children

According to the formula
M₁D₁ = M₂D₂
? 10 x 5 = (55/6) x D₂
? D₂ = 60/11 days
= 5⁵/₁₁ days

Work done by (x + y + z) in 1 day
= 50% = 1/2
Work done by x in 1 days = 20% = 1/5
Work done by y in 1 days = 25% = 1/4

? Work done by z in 1 day
= (1/2) - (1/5) - (1/4)
= (10 - 4 - 5)/20
= 1/20 = 5%

Y = 56 x (27/23) x (552/448)
=81

Extra men required =81-56
=25

Efficiency ( per minute) of Modi = 4 copies/min
Efficiency of Modi and Xerox together = 10 pages/min
? Efficiency of Xerox alone = 10 - 4 = 6 pages/min
? Mr. Xerox needs 6 min to copy 36 pages.

25 men and 15 women can complete, a piece of work in 12 days.
? Work done by them in 8 days = 8/12 = 2/3
Remaining work is completed by 25 men in 6 days
? Time taken by 25 men to complete the whole work = 3 x 6 = 18 days

From the question
Time taken by 15 women to complete the whole work = 1 / (1/12 - 1/18)
= 1 / {(3 - 2) / 36} = 36/(3 - 2) = 36 days

As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8
? Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24
? Work of (A + B) together for 3 days = 3 x (5/24) = 5/8
? Remaining work after 3 days = 1 - 5/8 = 3/8
? C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days
? Work of C for 1 day = 25/96 part.
? 25/96 part work can be done by C in 1 day
? 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 1¹¹/₂₅
? The complete day C did the work = 1 day.

Work of A for 1 day = 1/15
Work of B for 1 day = 1/20
Work of (A + B) together for 1 day = 1/15 + 1/20 = (4 + 3)/60 = 7/60
Remaining work after A alone does for 1 day = 1 - 1/15 = 14/15
? 7/60 part-work can be complete by (A + B) in 1 days
? 14/15 part-work can be completed by (A + B) in = (60/7) x (14/15) = 8 days.