A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

(B + C)'s 1 day's work =	❨	1	+	1	❩	=	7	.
		9		12			36

Work done by B and C in 3 days =	❨	7	x 3	❩	=	7	.
		36				12

Remaining work =	❨	1 -	7	❩	=	5	.
			12			12

Now,	1	work is done by A in 1 day.
	24

So,	5	work is done by A in	❨	24 x	5	❩	= 10 days.
	12				12

Formula: If A can do a piece of work in n days, then A's 1 day's work =	1	.
	n

(A + B + C)'s 1 day's work =	❨	1	+	1	+	1	❩	=	7	.
		24		6		12			24

Formula: If A's 1 day's work =	1	,	then A can finish the work in n days.
	n

So, all the three together will complete the job in	❨	24	❩ days	=	3	3	days.
		7				7

Let A's 1 day's work = x and B's 1 day's work = y.

Then, x + y =	1	and 16x + 44y = 1.
	30

Solving these two equations, we get: x =	1	and y =	1
	60		60

∴ B's 1 day's work =	1	.
	60

Hence, B alone shall finish the whole work in 60 days.

B's 10 day's work =	❨	1	x 10	❩	=	2	.
		15				3

Remaining work =	❨	1 -	2	❩	=	1	.
			3			3

Now,	1	work is done by A in 1 day.
	18

∴	1	work is done by A in	❨	18 x	1	❩	= 6 days.
	3				3

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x    ⟹ x =	❨	4 x 20	❩
		5

⟹ x = 16 days.

Hence, Tanya takes 16 days to complete the work.

Whole work is done by A in	❨	20 x	5	❩	= 25 days.
			4

Now,	❨	1 -	4	❩	i.e.,	1	work is done by A and B in 3 days.
			5			5

Whole work will be done by A and B in (3 x 5) = 15 days.

A's 1 day's work =	1	, (A + B)'s 1 day's work =	1	.
	25		15

∴ B's 1 day's work =	❨	1	-	1	❩	=	4	=	2	.
		15		25			150		75

So, B alone would do the work in	75	= 37	1	days.
	2		2

Ratio of times taken by A and B = 100 : 130 = 10 : 13.

Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     ⟹     x =	❨	23 x 13	❩	⟹     x =	299	.
		10			10

A's 1 day's work =	1	;
	23

B's 1 day's work =	10	.
	299

(A + B)'s 1 day's work =	❨	1	+	10	❩	=	23	=	1	.
		23		299			299		13

Therefore, A and B together can complete the work in 13 days.

(A + B)'s 20 day's work =	❨	1	x 20	❩	=	2	.
		30				3

Remaining work =	❨	1 -	2	❩	=	1	.
			3			3

Now,	1	work is done by A in 20 days.
	3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

S.I. = Rs	❨	1200 x 10 x 1	❩	= Rs. 120.
		100

C.I. = Rs.	[	1200 x	❨	1 +	5	❩	2	- 1200	]	= Rs. 123.
					100

∴ Difference = Rs. (123 - 120) = Rs. 3.

Sum = Rs.	❨	50 x 100	❩	= Rs. 500.
		2 x 5

Amount	= Rs. [ 500 x ❨ 1 + 5 ❩ 2 ] 100
	= Rs. ❨ 500 x 21 x 21 ❩ 20 20
	= Rs. 551.25

∴ C.I. = Rs. (551.25 - 500) = Rs. 51.25