In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Let A = 2k, B = 3k and C = 5k.

A's new salary =	115	of 2k =	❨	115	x 2k	❩	=	23k
	100			100				10

B's new salary =	110	of 3k =	❨	110	x 3k	❩	=	33k
	100			100				10

C's new salary =	120	of 5k =	❨	120	x 5k	❩	= 6k
	100			100

∴ New ratio	❨	23k	:	33k	: 6k	❩	= 23 : 33 : 60
		10		10

Let the third number be x.

Then, first number = 120% of x =	120x	=	6x
	100		5

Second number = 150% of x =	150x	=	3x
	100		2

∴ Ratio of first two numbers =	❨	6x	:	3x	❩	= 12x : 15x = 4 : 5.
		5		2

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 : 15 : x

⟹ 5x = (8 x 15)

x =	(8 x 15)	= 24.
	5

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x - 3x = 1000

⟹ x = 1000.

∴ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

⟹

❨

140

x 5x

❩

,

❨

150

x 7x

❩

and

❨

175

x 8x

❩

100

100

100

⟹ 7x,	21x	and 14x.
	2

∴ The required ratio = 7x :	21x	: 14x
	2

⟹ 14x : 21x : 28x

⟹ 2 : 3 : 4.

(x x 5) = (0.75 x 8)   ⟹ x =	❨	6	❩	= 1.20
		5

Let the numbers be 3x and 5x.

Then,	3x - 9	=	12
	5x - 9		23

⟹ 23(3x - 9) = 12(5x - 9)

⟹ 9x = 99

⟹ x = 11.

∴ The smaller number = (3 x 11) = 33.

Suppose pipe A alone takes x hours to fill the tank.

Then, pipes B and C will take	x	and	x	hours respectively to fill the tank.
	2		4

∴	1	+	2	+	4	=	1
	x		x		x		5

⟹	7	=	1
	x		5

⟹ x = 35 hrs.

Let the cistern be filled by pipe A alone in x hours.

Then, pipe B will fill it in (x + 6) hours.

∴	1	+	1	=	1
	x		(x + 6)		4

⟹	x + 6 + x	=	1
	x(x + 6)		4

⟹ x² - 2x - 24 = 0

⟹ (x -6)(x + 4) = 0

⟹ x = 6.     [neglecting the negative value of x]

Part filled in 2 hours =	2	=	1
	6		3

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

∴ (A + B)'s 7 hour's work =	2
	3

(A + B)'s 1 hour's work =	2
	21

∴ C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=	❨	1	-	2	❩	=	1
		6		21			14

∴ C alone can fill the tank in 14 hours.