The average age of a woman and her daughter is 42 years. The ratio of their ages is 2 : 1 respectively. Find the daughter's age.

Let the present ages of Surabhi and Neerja are 6x and 7x years respectively.
According to question,
(6x + 6)/(7x + 6) = 15/17
? (6x + 6)x17 = 15x(7x + 6)
? 102x + 102 = 105x + 90
? 3x = 12
? x = 4
Hence, present ages of Neerja = 7 x 4 = 28 years

Let one year ago the ages of Yamini and Gamini were 6P and 7P years respectively; then
(6P + 5)/(7P + 5) = 7/8
? (6P + 5) x 8 = 7 x (7P + 5)
? 48P + 40 = 49P + 35
? P = 5
Hence, present ago of Gamini = 7P + 1 = 7 x 5 + 1 = 36 years

The ratio of Ram's and Mohan's present age is 7 : 5.
Let us assume the present ages of Ram and Mohan are 7Y and 5Y years.
2 Years ago the age of Ram and Mohan will be 7Y - 2 and 5Y - 2 years.
According to question,
Two years ago, the ratio of Ram's and Mohan's age was 3 : 2, then
(7Y -2)/(5Y - 2) = 3/2
? (7Y -2) x 2 = 3 x (5Y - 2)
? 14Y - 4 = 15Y - 6
? Y = 2
Hence, their present ages = 7 x 2 = 14 years and 5 x 2 = 10 year

Let us assume the present age of Radha be Y years; then
Before 6 years Radha's age will be Y - 6 years.
According to question,
Today her age is 1¹/₄ times her age at the time of marriage,
5/4 ( Y - 6 ) = Y ( Since 1¹/₄ = 5/4 )
? 5Y - 30 = 4Y
? Y = 30 years
Hence, her son's age = 30 x 1/10 =3 years

Method 1
Let the present age of B and A be x and ( x + 9 ) years; then,
Age of B and A after 10 years will be x + 10 and x + 9 + 10;
According to question,
In 10 years A will be twice as old as B was 10 years ago
2(x - 10) = x + 9 + 10
2x - 20 = x + 19
? 2x - x = 19 + 20
? x = 39 years

Method 2
Let us assume the present age of B and A be x and y years.
According to question,
A is now 9 years older than B,
y = x + 9...........(1)
Again according to question,
In 10 years A will be twice as old as B was 10 years ago
y + 10 = 2( x - 10)................. (2)
now put the value of y from equation (1) in above equation (2)
x + 9 +10 = 2x - 20
? 2x - x = 19 + 20
? x = 39 years
So Present age of B = 39 years.

Let the present ages of A and B are 11x and 13x years respectively; then
According to question,
After 7 years the ratio of their ages will be 20 : 23.
(11x + 7 ) / (13x + 7) = 20/23
? (11x + 7 ) 23 = 20 (13x + 7)
? 253x + 161 = 260x + 140
? 7x = 21
? x = 3
Hence, difference of their ages = 13x - 11x = 2x = 2 x 3 = 6 years

Let the present ages of A, B and C are 3x, 5x and 7x years respectively; then
According to question,
3x + 5x + 7x = 3 x 25
? 15x = 75
? x = 5
Hence, age of A = 3x = 3 x 5 = 15 years

Let us assume the present age of baby Y year.
According to question,
Three years ago, the average age of a family of 5 members was 17 years.
The present Total age of the family of 5 member = 5 x 17 + 5 x 3 =100 ..........(1)
Again according to question,
The average age of the family is the same as what was three years ago.
The present average age of family of 6 member= 17
Total present age of family of 6 member / 6 = 17
(Total present age of family of 5 member + present age of baby)/6 = 17
100 + Y = 17 x 6
Y = 17 x 6 - 100 = 102 - 100 = 2 years

3 Years age Ritu's age was x years, then
Ritu's present age = x + 3 years
According to question,
Present age of Rahul is 5 years less than Ritu's present age
Hence, present age of Rahul = x + 3 - 5 = x - 2 years

Let us assume the present age of son be x then his father present age will be 3x.
According to question,
Six years hence, the ratio of their ages will be 5 : 2 respectively
(3x + 6)/(x+6) = 5/2
? (3x + 6)2 = 5(x+6)
? 6x + 12 = 5x + 30
? x = 18
Hence, age of Sanyal = 3 x 18 = 54 years