Problems On Ages

Let the present ages of Abdul and Amitabh be A and M.
Given, A + M = 9 (A - M)
⇒ A + M = 9A - 9M
⇒ M + 9 M = 9A - A
⇒ 10M = 8A
⇒ 5M = 4A
⇒ A/M = 5/4
⇒ The ratio of present ages of Abdul and Amitabh, A : M = 5 : 4
⇒ present age of Abdul ie., A = 5x
present age of Amitabh ie., M = 4x
6 years hence,
(A + 6) + (M + 6) = 12 [(A + 6) - (M + 6)]
⇒ (5x + 6) + (4x + 6) = 12 [5x + 6 - 4x - 6]
⇒ 9x + 12 = 12 [x]
⇒ 12x - 9x = 12
⇒ 3x = 12
⇒ x = 4
Hence, present age of Abdul ie., A = 5x = 5 × 4 = 20 years

Given, the present age of Samrat = 8 years
Then, the present age of Nisha = present age of Samrat - 4 = 8 - 4 = 4 years
Given, Nisha is one-fifth times as old as Ashwin
⇒ present age of Nisha = (1/5) × present age of Ashwin
⇒ present age of Ashwin = 5 × present age of Nisha = 5 × 4 = 20 years
Given, Ashwin is 4 years younger than Pratap
Then, Pratap is 4 years older than Ashwin.
⇒ present age of Pratap = present age of Ashwin + 4 = 20 + 4 = 24 years
Now, present age of Nisha × 6 times = 4 × 6 = 24 which is Pratap's present age.
Thus, Pratap is 6 times older than Nisha.

Let A be the age of person 'A'
B be the age of person 'B'
and C be the age of person 'C'
Given, A = (1/6)B ⇒ eqn (1)
B + 10 = 2 (C + 10) ⇒ eqn (2)
If C's eighth birthday was celebrated two years ago, then present age of C must be 10 years.
Substitute C = 10 in eqn (2), we get
B + 10 = 2 (10 + 10)
⇒ B = 2 (20) - 10
⇒ B = 40 - 10
⇒ B = 30
Thus, present age of B = 30 years.
Now From eqn (1)
A = (1/6) × 30
⇒ A = 5
Hence, present age of A = 5 years.

Let present ages of Devika and Apsara be 4X and 7X respectively
Present age of Shalini = 7X + 4
sum of the present ages of Devika and Shalini is 48 years
⇒ 4X + (7X + 4) = 48
⇒ 11X = 44
⇒ X = 4
Present age of Shalini = 7X + 4 = 7×4 + 4 = 32
Shalini's age two years ago = 32 - 2 = 30

When Shree was born, Mother was 30.
She is 4 years younger to her brother, so brother was 4 years old.
Sister was 4 years old when brother was born, so sister is 4 years elder to brother, so sister was 8 years old.
Father was 30 when sister was born, so father is 30 years elder to sister, so father was 30+8 = 38 years old.
Now when Shree was born, mother was 30 and father was 38
So difference= 38-30 = 8 years.
So when mother was born, father was 8.

When Dhriti was born:
Mother was 30 when Dhriti born.
Dhriti is 4 years younger to her brother, so when Dhriti born her brother was 4 years old.
Her sister was 4 years old when brother was born, so sister is 4 years elder to brother, so sister was 8 years old when Dhriti born.
Father was 30 when sister was born, so father is 30 years elder to sister, so father was 30+8 = 38 years old when Dhriti born.
Now when Dhriti was born, mother was 30 and father was 38
So difference in their ages is 8 years. So when mother was born, father was 8.

Let the Shoba's age be 'x'.
Shoba's brother's age =×- 4
Shobha's father's age = x + 38
Shobha's mother's age = 36 + (x - 4) = 32 + x
Difference between Shobha's father and mother = (x + 38) - (32 + x)
= x + 38 - 32 - x
= 6 years:

Let the daughter's present age be×yr.
father's age is 3 years more than three times the age of his daughter.
Father's age = 3x + 3
Accoroding to the question, after 3 years
Father's age = 10 yr more than twice the age of the daughter
(3x + 3) + 3 = 2(x + 3) + 10
3x + 6 = 2x + 6 + 10
3x + 6 = 2x + 16
3x - 2x = 16 - 6
x = 10
∴ father's present age = 3x + 3 = 3(10) + 3 = 33 years.

Let the age of Arnav's brother be 'a'.
Arnav age = a + 8
Mother's age = a + 24
Given, the ratio between the ages of Arnav and their mother is 7 : 11.
(a + 8)/(a + 24) = 7/11
(a + 8)11 = (a + 24)7
11a + 88 = 7a + 168
11a - 7a = 168 - 88
4a = 80
a = 20
Hence, Arnav's brother present age = 20 yrs
∴ Arnav's brother age after 3 years = 20 + 3 = 23 yearss:

Let the present age of mother be×and present age of daughter be y.
Given, 1 yr ago mother's age = 4 times of daughter's age
x - 1 = 4(y - 1)
x - 1 = 4y - 4
x = 4y - 3
And also given, after 6 yrs mother's age = double the daughter's age by five yrs
x + 6 = 2(y + 6) + 5
(4y - 3) + 6 = 2y + 12 + 5
4y + 3 = 2y + 17
4y - 2y = 17 - 3
2y = 14
y = 7 yrs
∴ mother's age = 4(7) - 3 = 28 - 3 = 25 yrs
Required ratio of present age of mother and daughter = 25 : 7.