A, B, C, D, are four friends. Average age of A and C is 35 years and that of B, and D is 40 years. Average age of B, C and D is 40 years. The sum of the ages of A and D is equal to that of B and C. Find out the ages (in years) of A, B, C and D.

According to question ,
The average age of a cricket team = 27 years
Age of two old players = 24 + 27 = 51
Age of two new players = 23 + 28 = 51
? New average age of a cricket team = 27 + ( Age of two old players ) - ( Age of two new players )
New average age of a cricket team = 27 + ( 51 ) - ( 51 ) = 27 years
In other words ,The total age of the two players which were replaced is the same as that of the total age of two players which replaced them. Therefore, the new average will remain unchanged.

Let us assume the present age of the subordinate is P then her subordinate age will be (P + 16).
According to Question,
Four years ago, the respective ratio of the ages of the boss and subordinate was 11 : 7.
(P +16 - 4 )/ (P - 4) = 11/7
? 7 x (P +16 - 4 ) = 11 x (P - 4)
? 7 x (P +12 ) = 11 x (P - 4)
? 7P + 84 = 11P - 44
? 4P = 128
? P = 32 years

Let us assume the present age of Ram R, Shyam S and Mohan M.
5 years ago, Ram age = R - 5
5 years ago, Shyam age = S - 5
5 years ago, Mohan age = M - 5
According to question,
5 years ago, the average age of Ram and Shyam was 20 years,
(5 years ago, Ram age + 5 years ago, Shyam age) /2 = 20
(R - 5 + S - 5 )/2 = 20
R + S = 40 + 10 = 50 ................(1)
Now Again according to question,
Now , the average age of Ram, Shyam and Mohan is 30 years
(R + S + M)/3 = 30
R + S + M = 90
Pu the value of R + S from equation (1)
50 + M = 90
M = 90 - 50 = 40
The present age of Mohan = 40 years
10 years hence, the age of Mohan = 40 + 10 = 50 years

Let the present ages of Shami, Nammi and pammi are 3x, 4x and 5x years respectively;
then, According to question,
3x + 4x + 5x = 48
? 12x = 48
? x= 4
Hence, their present ages are 12, 16 and 20 years respectively.
So, required ratio = (12 + 8) : (16 + 8) : (20 + 8) = 20 : 24 : 28 = 5 : 6 : 7

According to question ,
Mother's age - Sum of her two daughters' age = 6.
The average age of two daughters = 22
Total age of two daughters = 22 × 2 = 44 years
? The age of their mother = Total age of two daughters + 6 years
The age of their mother = 44 + 6 = 50 years

According to question ,
Age of his wife = 35 years
Age of his son = 7 years and Age of man = 32 years
At the birth of son, The age of mother = Age of his wife - Age of his son = 35 ? 7 = 28 years
Difference in age = Age of man - age of mother = 32 ? 28 = 4 years

Suppose the age of Naresh's brother = P years
According to question ,
? Age of Naresh = 2 × age of Naresh's brother ? 4
Therefore , Age of Naresh = 2P ? 4

Suppose my age = P years
My father's age = my age + 21 years = P + 21 years
Again After 12 years ,
2 ( my age + 12 ) = My father's age + 12
? 2 (P + 12) = (P + 21) + 12
? 2P + 24 = P + 33
? P = 33 ? 24 = 9 years
Hence , I am 9 years old now .