X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

(20 x 16) women can complete the work in 1 day.

∴ 1 woman's 1 day's work =	1	.
	320

(16 x 15) men can complete the work in 1 day.

∴ 1 man's 1 day's work =	1
	240

So, required ratio	= 1 : 1 240 320
	= 1 : 1 3 4
	= 4 : 3 (cross multiplied)

(A + B)'s 1 day's work =	1
	10

C's 1 day's work =	1
	50

(A + B + C)'s 1 day's work =	❨	1	+	1	❩	=	6	=	3	. .... (i)
		10		50			50		25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) =	3
	25

⟹ A's 1 day's work =	3	.
	50

∴ B's 1 day's work	❨	1	-	3	❩	=	2	=	1	.
		10		50			50		25

So, B alone could do the work in 25 days.

Number of pages typed by Ravi in 1 hour =	32	=	16	.
	6		3

Number of pages typed by Kumar in 1 hour =	40	= 8.
	5

Number of pages typed by both in 1 hour =	❨	16	+ 8	❩	=	40	.
		3				3

∴ Time taken by both to type 110 pages =	❨	110 x	3	❩	hours
			40

= 8	1	hours (or) 8 hours 15 minutes.
	4

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

∴ P's1 hour's work =	1	and Q's 1 hour's work =	1	.
	96		80

(P + Q)'s 1 hour's work =	❨	1	+	1	❩	=	11	.
		96		80			480

So, both P and Q will finish the work in	❨	480	❩	hrs.
		11

∴ Number of days of 8 hours each =	❨	480	x	1	❩	=	60	days = 5	5	days.
		11		8			11		11

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y =	1	and 3x + 7y =	1	.
	8		10

Solving the two equations, we get: x =	11	, y =	1
	400		400

∴ 1 woman's 1 day's work =	1	.
	400

⟹ 10 women's 1 day's work =	❨	1	x 10	❩	=	1	.
		400				40

Hence, 10 women will complete the work in 40 days.

A's 1 day's work =	1	;
	15

B's 1 day's work =	1	;
	20

(A + B)'s 1 day's work =	❨	1	+	1	❩	=	7	.
		15		20			60

(A + B)'s 4 day's work =	❨	7	x 4	❩	=	7	.
		60				15

Therefore, Remaining work =	❨	1 -	7	❩	=	8	.
			15			15

C's 1 day's work =	1	-	❨	1	+	1	❩	=	1	-	7	=	1	.
	3			6		8			3		24		24

A's wages : B's wages : C's wages =	1	:	1	:	1	= 4 : 3 : 1.
	6		8		24

∴C's share (for 3 days) = Rs.	❨	3 x	1	x 3200	❩	= Rs. 400.
			24

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes	❨	3	x 60	❩	= 90 days.
		2

So, A takes 30 days to do the work.

A's 1 day's work =	1
	30

B's 1 day's work =	1
	90

(A + B)'s 1 day's work =	❨	1	+	1	❩	=	4	=	2
		30		90			90		45

∴ A and B together can do the work in	45	= 22	1	days.
	2		2

(A + B + C)'s 1 day's work =	1	;
	6

(A + B)'s 1 day's work =	1	;
	8

(B + C)'s 1 day's work =	1	.
	12

∴ (A + C)'s 1 day's work	= ❨ 2 x 1 ❩ - ❨ 1 + 1 ❩ 6 8 12
	= ❨ 1 - 5 ❩ 3 24
	= 3 24
	= 1 . 8

So, A and C together will do the work in 8 days.

(P + Q + R)'s 1 hour's work =	❨	1	+	1	+	1	❩	=	37	.
		8		10		12			120

Work done by P, Q and R in 2 hours =	❨	37	x 2	❩	=	37	.
		120				60

Remaining work =	❨	1 -	37	❩	=	23	.
			60			60

(Q + R)'s 1 hour's work =	❨	1	+	1	❩	=	11	.
		10		12			60

Now,	11	work is done by Q and R in 1 hour.
	60

So,	23	work will be done by Q and R in	❨	60	x	23	❩	=	23	hours ≈ 2 hours.
	60			11		60			11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.