Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

(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.

2(A + B + C)'s 1 day's work =	❨	1	+	1	+	1	❩	=	15	=	1	.
		30		24		20			120		8

Therefore, (A + B + C)'s 1 day's work =	1	=	1	.
	2 x 8		16

Work done by A, B, C in 10 days =	10	=	5	.
	16		8

Remaining work =	❨	1 -	5	❩	=	3	.
			8			8

A's 1 day's work =	❨	1	-	1	❩	=	1	.
		16		24			48

Now,	1	work is done by A in 1 day.
	48

So,	3	work will be done by A in	❨	48 x	3	❩	= 18 days.
	8				8

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.

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.