A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

(A + B + C)'s 1 day's work =	1	,
	4

A's 1 day's work =	1	,
	16

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

∴ C's 1 day's work =	1	-	❨	1	+	1	❩	=	❨	1	-	7	❩	=	5	.
	4			16		12				4		48			48

So, C alone can do the work in	48	= 9	3	days.
	5		5

(A's 1 day's work) : (B's 1 day's work) =	7	: 1   =   7 : 4.
	4

Let A's and B's 1 day's work be 7x and 4x respectively.

Then, 7x + 4x =	1	⟹     11x =	1	⟹     x =	1	.
	7		7		77

∴ A's 1 day's work =	❨	1	x 7	❩	=	1	.
		77				11

Work done by X in 8 days =	❨	1	x 8	❩	=	1	.
		40				5

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

Now,	4	work is done by Y in 16 days.
	5

Whole work will be done by Y in	❨	16 x	5	❩	= 20 days.
			4

∴ X's 1 day's work =	1	, Y's 1 day's work =	1	.
	40		20

(X + Y)'s 1 day's work =	❨	1	+	1	❩	=	3	.
		40		20			40

Hence, X and Y will together complete the work in	❨	40	❩	= 13	1	days.
		3			3

Let the distance travelled by x km.

Then,	x	-	x	= 2
	10		15

⟹ 3x - 2x = 60

⟹ x = 60 km.

Time taken to travel 60 km at 10 km/hr =	❨	60	❩hrs	= 6 hrs.
		10

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

∴ Required speed =	❨	60	❩kmph.	= 12 kmph.
		5

Let distance = x km and usual rate = y kmph.

Then,	x	-	x	=	40	⟹   2y(y + 3) = 9x ....(i)
	y		y + 3		60

And,	x	-	x	=	40	⟹   y(y - 2) = 3x ....(ii)
	y -2		y		60

On dividing (i) by (ii), we get: x = 40.

A's 2 day's work =	❨	1	x 2	❩	=	1	.
		20				10

(A + B + C)'s 1 day's work =	❨	1	+	1	+	1	❩	=	6	=	1	.
		20		30		60			60		10

Work done in 3 days =	❨	1	+	1	❩	=	1	.
		10		10			5

Now,	1	work is done in 3 days.
	5

∴ Whole work will be done in (3 x 5) = 15 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

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.

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

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