A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

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

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

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

Work done by X in 4 days =	❨	1	x 4	❩	=	1	.
		20				5

Remaining work =	❨	1 -	1	❩	=	4	.
			5			5

(X + Y)'s 1 day's work =	❨	1	+	1	❩	=	8	=	2	.
		20		12			60		15

Now,	2	work is done by X and Y in 1 day.
	15

So,	4	work will be done by X and Y in	❨	15	x	4	❩	= 6 days.
	5			2		5

Hence, total time taken = (6 + 4) days = 10 days.

(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)

(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.

1 woman's 1 day's work =	1
	70

1 child's 1 day's work =	1
	140

(5 women + 10 children)'s day's work =	❨	5	+	10	❩	=	❨	1	+	1	❩	=	1
		70		140				14		14			7

∴ 5 women and 10 children will complete the work in 7 days.

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B's 1 day's work =	1	.
	12

∴ A's 1 day's work =	1	; (2 times of B's work)
	6

(A + B)'s 1 day's work =	❨	1	+	1	❩	=	3	=	1	.
		6		12			12		4

So, A and B together can finish the work in 4 days.

Suppose A, B and C take x,	x	and	x	days respectively to finish the work.
	2		3

Then,	❨	1	+	2	+	3	❩	=	1
		x		x		x			2

⟹	6	=	1
	x		2

⟹ x = 12.

So, B takes (12/2) = 6 days to finish the work.

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

Then, 6x + 8y =	1	and 26x + 48y =	1	.
	10		2

Solving these two equations, we get : x =	1	and y =	1	.
	100		200

(15 men + 20 boy)'s 1 day's work =	❨	15	+	20	❩	=	1	.
		100		200			4

∴ 15 men and 20 boys can do the work in 4 days.