Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how, many days will all of them together complete the remaining work

(A + B)'s 5 day's work = 5 x (1/10 + 1/20) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/20 work is done by B in = 1 day
? 1/4 work is done by B in = 20 x (1/4) i.e., 5 days.

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.

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.

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

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.

(B + C)'s 2 day's work = 2 x (1/10 + 1/15) = 1/3
Remaining work = (1 - 1/3) = 2/3
? 1/9 work is done by A in 1 day
? 2/3 work is done by A in (9 x 2) / 3 = 6 days

24 men complete the work in 16 days
? Work that 16 men complete in 12 days = (16/24) x (12/ 16) = 1/2 part of work in 12 days.

32 women complete the work in 24 days
? Work that 16 women complete in 14 days = (16/32) x (14/24) = 7/24 part of work in (12 + 2) = 14 days.

So, the remaining part of the work which done by (sixteen men + sixteen women) and required additional no. of men in 2 days = 1 - (1/2 + 7/24) = 1/2 - 7/24 = 5/24 (part)

Now, in 2 days 5/24 part part of the work is done by (24 x 16)/ 2 x (5/ 24) = 40 men
? Required additional no. of men = 40 - 16 =24.

Work of (A + B + C) for 1 hour = 1/16 + 1/20 + 1/24 = 37/240
? Work of (A + B + C) for 4 hours = 4 x 37/240 = 37/60
? Remaining work = 1 - 37/60 = 23/60
? Work of (B + C) for 1 hour = 1/20 + 1/24 = 11/120

? 11/120 work is done by (B + C) in 1 hour
? 23/60 work is done by (B + C) = 120/11 x 23/60 = 46/11 hours = 4 hours 11 min.
? The type at which the report was typed = 01 : 00 + 04 : 11 = 05 : 11 p.m.

? 14 person complete in 16 days = 1 work
? 8 person complete in 12 days = 1 x (8/14) x (12/16) = 3/7
? Remaining work = 1 - 3/7 = 4/7
and total number of person = 8 + 8 = 16
? 14 person do 1 work in 16 days
? 16 person do 4/7 work in 16 x (14/16) x (4/7) = 8 days

5 men + 3 boys can reap 23 hectares in 4 days ......(i)
3 men + 2 boys can reap 7 hectares in 2 days ......(ii)

? From (i),
14( 5 men + 3 boys) can reap 23 x 14 hectares in 4 days
Now, from (ii)
? 23 (3 men + 2 boys) can reap 7 x 2 x 23 hectares in 4 days

? 14(5 men + 3 boys) = 23 (3 men + 2 boys)
? 70 men + 42 boys = 69 men + 46 boys
? 1 men = 4 boys
Now, 5 men + 3 boys = 23 boys

? 23 boys can reap 23 hectare 4 days
? 1 boy can reap 1 hectares in 4 days
? 4 boys can reap 1 hectare in 1 day
? 4 x 45 boys can reap 45 hectaes in 1 day
? 4 x 45 / 6 boys can reap 45 hectares in 6 days
? 30 boys can reap 45 hectares in 6 days

But 30 boys = 28 boys + 2 boys = 7 men + 2 boys
Hence, 2 boys can assist 7 men for the work.