A and B can complete a work in 12 days and 18 days, respectively. A begins to do the work and they work alternately one at a time for 1 days each. The whole work will be completed in how many 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%

Let A takes x and B takes 3N days to finish the job.
According to the question,
3N - N = 30
? N = 30/2 = 15 days
? B's time to complete the work = 3N
= 3 x 15 = 45 days

? (A + B)'s 1 day's work
= (1/15) + (1/45) = (3 + 1)/45 = 4/45
? (A + B) will finish the work in 4/45 days
? Required time = 4/45 = 11¹/₄

A,s 1 days work =1/8
B's 1 day's work in breaking the building = 1/3
Now, according to the question,
A's 4 day's work = 4 x (1/8) = 1/2
Now, A's and B's 2 day's work
= 2[(1/8) - (1/3)] = 2 x (-5/24) = -10/24
Total work done in 6 days = 1/2 + (-10/24) = (12 - 10)/24 = 2/24 = 1/12
Remaining work = 1 - (1/12) = 11/12
Now, A has complete the work, so A can complete in N days.
(1/8) x N = 11/12
? N = (11 x 8) / 12
N = (11 x 2)/3 = 7¹/₃ days

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.