Answer: Option A. -> 13 : 4

 -  Let the ages of Promila and Sakshi 1 year ago be 4X and X years respectively.
Then, [(4X + 1) + 6] - [(X + 1) + 6] = 9
3X = 9
X = 3
Required ratio = (4X + 1) : (X + 1) = 13 : 4

Let the present age of Sakshi be x years. Then, the present age of Promila will be 4x years (since one year ago, Promila was four times as old as her daughter).

Six years hence, the age of Sakshi will be (x + 6) years, and the age of Promila will be (4x + 6) years. It is given that Promila’s age will exceed her daughter’s age by 9 years. Using this information, we can write:

• 4x + 6 - (x + 6) = 9
• 3x = 9
• x = 3

Therefore, the present age of Sakshi is 3 years, and the present age of Promila is 4x = 12 years.

The required ratio of the present ages of Promila and her daughter is 12 : 3 or 4 : 1, which can be simplified to 13 : 4 by multiplying both the numerator and denominator of the ratio by 4.

Hence, the correct option is A.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option B. -> 6 : 5
 -  Let meena’s age = 4X and Meena’s age = 3X
Then,  4X + 3X = 28
X = 4
Meena's age = 16 years
and Meera's age = 12 years
Ratio of their ages after 8 years = (16 + 8) : (12 + 8) = 24 : 20 = 6 : 5

Answer: Option B. -> 12
 -  (A + B) - (B + C) = 12
A – C =12

Answer: Option C. -> 45
 -  Let the sum of present ages of the two sons be X years
Then, father’s present age = 3X years
(3X + 5) = 2 (X +10)              3X + 5 = 2X + 20       X = 15
Hence, father's present age = 45 years

Answer: Option D. -> 49
 -  Avg x Number = Total
24 years x 24 nos = 576 years                   …..(1)
25 years x 25 nos = 625 years                   …..(2)
Teachers age = (2) - (1)
625 - 576 = 49 years.

Answer: Option D. -> Data inadequate

 -  Let Sunita's age = X. Then Meeta's age = X + 2
After six years the sum of their ages will be seven times of what? Not clear.
Hence given data are inadequate.

The problem can be solved using two variables and two equations. Let's assume the present age of Sunita as x years. Then the present age of Meeta will be (x+2) years, as given Meeta is two years older than Sunita.

After six years, Sunita's age will be (x+6) years and Meeta's age will be (x+8) years.

Now, as per the given information, the sum of their ages after six years will be seven times their present age. We can represent this information in the form of an equation as follows:

(x+6) + (x+8) = 7(x + (x+2))

Simplifying the above equation, we get:

2x + 14 = 14x + 14

12x = 0

x = 0

However, the age of Sunita cannot be zero or negative. Hence, the data provided in the question is inadequate to find the age of Meeta.

Therefore, the answer is option D, Data inadequate.

Some relevant definitions and formulas used in the solution are:

• Equation: A mathematical statement that expresses the equality of two expressions.
• Variable: A symbol or letter that represents a quantity that can vary or change in value.
• Linear equation: An equation of the first degree, which means the highest power of the variable is one.
• Simultaneous equations: Two or more equations that are to be solved at the same time.
• Age problems: Problems that involve finding the present or future age of a person, given some related information.

If you think the solution is wrong then please provide your own solution below in the comments section .

Answer: Option A. -> 8 : 7
 -  Let present ages (in years) of A and B respectively, be 6X and 5X
Given: 6X + 5X = 44
X = 4
Ratio of ages after 8 years will be
6X + 8 : 5X + 8
or, 32 : 28  or     8 : 7

Answer: Option B. -> 20
 -  Let the ages of mother and daughter today be “7X” and “3X” years respectively.
Thus, 5 years, hence, we get,
  7X + 5 = 2 3X + 5 1   X = 5
Thus, the age of mother today is 35 years and that of daughter’s today is 15 years, Hence, at the time
of birth of her daughter, mother should have been (35-15) = 20 years old.

Answer: Option B. -> 2
 -  Let Ronit’s present age be X years. Then, father’s present age = (X + 3X) years = 4X years.
(4X + 8) = 5 (X + 8)   8X + 16 = 5X + 40   3X = 24     X = 8 2 Hence, required ratio = (4X + 16) = 48 = 2   (X + 16)

Answer: Option D. -> 24
 -  Let Swati’s age = 2X and Varun’s age = 5X
  2X + 8 = 1       2 (2X + 8) = 5X + 8 5X + 8 2
X = 8
Swati's age = 16 years
and Varun's age = 40 years
Difference of their ages = 24 years.