According to the question:

6x + 5x = 55

⇒ 11x = 55

⇒ x = 5

∴ Gyanendra’s age after 7 years = 6(5) + 7 = 37 years

Arbind’s age after 7 years = 5(5) + 7 = 32 years

∴ Required ratio = 37 : 32

Hence, option B is the correct answer.

According to the question:

F – S = 15

F = S + 15 …..(i)

And, F – 5 = 2(S – 5)

⇒ S + 15 – 5 = 2(S – 5)  [From (i)]

⇒ S + 10 = 2S – 10

⇒ S = 20 years

∴ F = 20 + 15 = 35 years

Hence, option A is the correct answer.

Let the present age of father, mother and son be 8x , 5x and 2x respectively.

According to the question,

8x = 48

Or, x = 48/8 = 6

Age of father after 3 years = 48 + 3 = 51 years 

Age of mother after 3 years = 5x + 3 = 30 + 3 = 33 years 

Age of son after 3 years = 2x + 3 = 12 + 3 = 15 years 

Sum of age of father, mother, and son after 3 years = 51 + 33 + 15 = 99 years

Average age = 99/3 = 33 years

Hence, option C is the correct answer.

The ratio of a father’s age to his son’s age is 3 : 2.

Let the age of father and son be 3x and 2x.

According to the question:

(3x)(2x) = 486

⇒ x² = 81

⇒ x = 9

Father’s age = 3(9) = 27 years

Son’s age = 2(9) = 18 years.

Required ratio = (27 + 5) : (18 + 5)

= 32 : 23

Hence, option D is the correct answer.

Nalini's younger brother is 12 years old.

The ratio of the age of Nalini to that of her brother is 7 : 6.

Let age of Nalini = 7x

Age of Nalini’s brother = 6x

According to question:

⇒ 6x = 12 years

⇒ x = 2 years

Age of Nalini = 14 years

Age of Nalini’s brother = 12 years

Ratio in their ages 6 years hence = 14+6 : 12+6 = 20 : 18 = 10 : 9

Let the present age of Kunal = x years

And the present age of kirti = y years

Now, according to question,

(y + 6) = 2(x + 6)

 y + 6 = 2x + 12

 y - 2x = 12 – 6

 y – 2x = 6           …..eq1

Now,

4 years ago, age of Kunal = (x – 4) years and age of Kirti = (y – 4) years

y – 4 = 4(x – 4)

 y – 4 = 4x – 16

 4x – y = 16 – 4

 4x – y = 12          …..eq2           

By adding eq1 and eq2

4x – 2x = 6 + 12

 2x = 18

 x = 9 years

Therefore, the present age of Kunal = 9 years

Total present age of husband, wife, and child

= 27 × 3 + 3 × 3 = 81 + 9 = 90 years

Present age of wife and child

= 20 × 2 + 5 × 2 = 40 + 10 = 50 years

∴ Present age of the husband will be

= 90 – 50 = 40 years

Let the age of Deepika, Heera, and Arjit are d, h and a respectively.

Given, h =  and a = 1.5h + 3 = + 3

Also, 5d = 3a

By putting the value of a above,

5d = 3 × {+3}

5d = 3 × (d + 15 + 3)

5d = 3 × (d + 18)

5d = 3d + 54

5d – 3d = 54

2d = 54

d = 54/2 = 27

∴ h = × 27 + 10 = 2 × 9 + 10 = 18 + 10 = 28

And a = × d = ×27 = 5 × 9 = 45

Now total age of Arjit, Deepika and Heera will be

27 + 28 + 45 = 100 years

Two pipes S and U can fill a cistern in 24 hours and 30 hours respectively.

Let capacity of cistern = LCM (24, 30) = 120 unit

Efficiency of S = 120/24 = 5 units/hr

Efficiency of U = 120/30 = 4 units/hr

Let pipe U turned off after x hours. Then,

9x + 5(16−x) = 120

4x = 40

x = 10

Hence, pipe U turned off after 10 hours.

Let the fourth proportional of 12 , 16 and 5 be  x.

⇒ 12/16 = 5/x

→ x = (5×16)/12 = 20/3

And also  when  20, y, 15, 21 are in proportion.

Then, 20/y = 15/21

⇒   y = (20×21)/5

⇒  y =  28

Hence   ( 6x – y ) = 6(20/3) – 28

 =  40 – 28

= 12