Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

Let 40% of A =	2	B
	3

Then,	40A	=	2B
	100		3

⟹	2A	=	2B
	5		3

⟹	A	=	❨	2	x	5	❩	=	5
	B			3		2			3

∴ A : B = 5 : 3.

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

⟹	❨	120	x 7x	❩	and	❨	110	x 8x	❩
		100					100

⟹	42x	and	44x
	5		5

∴ The required ratio =	❨	42x	:	44x	❩	= 21 : 22.
		5		5

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 =	❨	5 x	3	❩	:	❨	8 x	3	❩	= 3 :	24
			5					5			5

⟹ A : B : C = 2 : 3 :	24	= 10 : 15 : 24
	5

⟹ B =	❨	98 x	15	❩	= 30.
			49

   1|1.5625( 1.25
    |1
    |-------
  22| 56
    | 44
    |-------
 245| 1225
    | 1225
    |-------
    |    X
    |-------     

∴ √1.5625 = 1.25.

√4a² - 4a + 1 + 3a = √(1)² + (2a)² - 2 x 1 x 2a + 3a

   = √(1 - 2a)² + 3a

   = (1 - 2a) + 3a

   = (1 + a)

   = (1 + 0.1039)

   = 1.1039

Given ratio = ½ : ⅔ : ¾ = 6 : 8 : 9.

∴ 1st part = Rs.	❨	782 x	6	❩	= Rs. 204
			23

	4	A	=	2	B
	15			5

⟹ A =	❨	2	x	15	❩B
		5		4

⟹ A =	3	B
	2

⟹	A	=	3
	B		2

⟹ A : B = 3 : 2.

∴ B's share = Rs.	❨	1210 x	2	❩	= Rs. 484.
			5

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.

Then, sum of their values = Rs.	❨	25x	+	10 x 2x	+	5 x 3x	❩	= Rs.	60x
		100		100		100			100

∴	60x	= 30	⟺  x =	30 x 100	= 50.
	100			60

Hence, the number of 5 p coins = (3 x 50) = 150.

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.

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.