The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

C.I.	= Rs. [ 4000 x ❨ 1 + 10 ❩ 2 - 4000 ] 100
	= Rs. ❨ 4000 x 11 x 11 - 4000 ❩ 10 10
	= Rs. 840.

∴ Sum = Rs.	❨	420 x 100	❩	= Rs. 1750.
		3 x 8

[

15000 x

❨

1 +

R

❩

2

- 15000

]

-

❨

15000 x R x 2

❩

= 96

100

100

⟹ 15000	[	❨	1 +	R	❩	2	- 1 -	2R	]	= 96
				100				100

⟹ 15000	[	(100 + R)2 - 10000 - (200 x R)	]	= 96
		10000

⟹ R2 =	❨	96 x 2	❩	= 64
		3

⟹ R = 8.

∴ Rate = 8%.

Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be n years.

Then, 30000	❨	1 +	7	❩	n	= 34347
			100

⟹	❨	107	❩	n	=	34347	=	11449	=	❨	107	❩	2
		100				30000		10000			100

∴ n = 2 years.

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

∴ R =	❨	100 x 60	❩	= 10% p.a.
		100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

∴ C.I.	= Rs. [ 12000 x { ❨ 1 + 10 ❩ 3 - 1 ] ] 100
	= Rs. ❨ 12000 x 331 ❩ 1000
	= 3972.

P

❨

1 +

20

❩

n

> 2P

⟹

❨

6

❩

n

> 2.

100

5

Now,	❨	6	x	6	x	6	x	6	❩	> 2.
		5		5		5		5

So, n = 4 years.

Ratio of initial investments =	❨	7	:	4	:	6	❩	= 105 : 40 : 36.
		2		3		5

Let the initial investments be 105x, 40x and 36x.

∴ A : B : C =	❨	105x x 4 +	150	x 105x x 8	❩	: (40x x 12) : (36x x 12)
			100

   = 1680x : 480x : 432x = 35 : 10 : 9.

Hence, B's share = Rs.	❨	21600 x	10	❩	= Rs. 4000.
			54

Let B's capital be Rs. x.

Then,	❨	3500 x 12	=	2	❩
		7x		3

⟹ 14x = 126000

⟹ x = 9000.

A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.

∴ B's share = Rs.	❨	25000 x	3	❩	= Rs. 7,500.
			10

Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.

Let the initial investments of A and B be 3x and 5x.

A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.